How many 3-letter words can be formed using a, b, c, d, e if repetition is not allowed

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  • How many words can be formed from a letter SIGNATURE?
  • How many words can be formed using letter SIGNATURE such that vowels come together?
  • How many 3 letter words can be formed from SIGNATURE if repetition of letters is not allowed?
  • How many 3 letter words can be formed out of the letters of the word SIGNATURE?
  • How many 3 letter words can be formed from SIGNATURE if repetition is not allowed?
  • How many 3 letter words can be formed using Abcde if I repetition is not allowed II repetition is allowed?
  • How many 3 letter words with or without meaning can be formed using the letters of the word flash?
  • How many 3 letter words with or without meaning can be formed out of the letters of the word Monday when repetition of words is allowed?
  • How many 3 letter words can be formed using a b/c d/e if I repetition is not allowed II repetition is allowed?
  • How many 4 letter words can be formed using a b/c d and e if repetition of letters is allowed?
  • How many 3 letter words can be made if letters can be repeated?
  • How many 3 letter words can be formed from the letters Abcde if letters can be repeated in a word?

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  • Related Posts
  • How many words can be formed from a letter SIGNATURE?
  • How many words can be formed using letter SIGNATURE such that vowels come together?
  • How many 3 letter words can be formed from SIGNATURE if repetition of letters is not allowed?
  • How many 3 letter words can be formed out of the letters of the word SIGNATURE?
  • How many 3 letter words can be formed from SIGNATURE if repetition is not allowed?
  • How many 3 letter words can be formed using Abcde if I repetition is not allowed II repetition is allowed?
  • How many 3 letter words with or without meaning can be formed using the letters of the word flash?
  • How many 3 letter words with or without meaning can be formed out of the letters of the word Monday when repetition of words is allowed?

Nội dung chính

  • Related Posts
  • How many words can be formed from a letter SIGNATURE?
  • How many words can be formed using letter SIGNATURE such that vowels come together?
  • How many 3 letter words can be formed from SIGNATURE if repetition of letters is not allowed?
  • How many 3 letter words can be formed out of the letters of the word SIGNATURE?
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Exercise 1


  1. In how many ways can the letters of the word 'APPLE' be arranged ?

      A. 720
      B. 120
    C. 60
      D. 180

    Answer & Explanation

    Answer: Option C

    Explanation:

    The word 'APPLE' contains 5 letters, 1A, 2P, 1L.and 1E.

    $$\therefore$$ Required number of ways = $$\frac{5 !}{(1 !) (2 !) (1 !) (1 !)}$$ = 60.

  2. How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed ?

      A. 40
      B. 400
    C. 5040
      D. 2502

    Answer & Explanation

    Answer: Option C

    Explanation:

    'LOGARITHM' contains 10 different letters.

    Required number of words = Number of arrangements of 10 letters, taking 4 at a time = 10P4 = (10 * 9 * 8 * 7) = 5040.

  3. The value of 75P2 is :

      A. 2775
      B. 150
    C. 5550
      D. None of these

    Answer & Explanation

    Answer: Option C

    Explanation: 75P2 = $$\frac{75 !}{(75 - 2)!}$$ = $$\frac{75 !}{73 !}$$ = $$\frac{75 * 74 * (73 !)}{73 !}$$ = (75 * 74) = 5550.

  4. In how many ways can the letters of the word 'LEADER' be arranged ?

      A. 72
      B. 144
    C. 360
      D. 720

    Answer & Explanation

    Answer: Option C

    Explanation:

    The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.

    $$\therefore$$ Required number of ways = $$\frac{6 !}{(1 !)(2 !)(1 !)(1 !)(2!)}$$ = 360.

  5. How many words with or without meaning, can be formed by using all the letters of the word, 'DELHI', using each letter exactly once ?

      A. 10
      B. 25
      C. 60
    D. 120

    Answer & Explanation

    Answer: Option D

    Explanation:

    The word 'DELHI' contains 5 different letters.

    Required number of words = Number of arrangements of 5 letters, taken all at a time = 5P5 = 5 ! = (5 *4 *3 *2 *1) = 120.

  6. In how many different ways can the letters of the word 'RUMOUR' be arranged ?

    A. 180
      B. 90
      C. 30
      D. 720

    Answer & Explanation

    Answer: Option A

    Explanation:

    The word 'RUMOUR' contains 6 letters, namely 2R, 2U, 1M and 1U.

    $$\therefore$$ Required number of ways = $$\frac{6 !}{(2 !) (2 !) (1 !) (1!)}$$ = 180.

  7. How many arrangements can be made out of the letters of the word 'ENGINEERING' ?

    A. 277200
      B. 92400
      C. 69300
      D. 23100

    Answer & Explanation

    Answer: Option A

    Explanation:

    The word 'ENGINEERING' contains 11 letters, namely 3E, 3N, 2G, 2I and 1R.

    $$\therefore$$ Required number of arrangements = $$\frac{11 !}{(3 !) (3 !) (2 !)(2 !)(1 !)}$$ = 277200.

  8. How many words can be formed from the letters of the word 'SIGNATURE' so that the vowels always come together ?

      A. 720
      B. 1440
      C. 2880
    D. 17280

    Answer & Explanation

    Answer: Option D

    Explanation:

    The word 'SIGNATURE' contains 9 different letters.

    When the vowels IAUE are taken together, they can be supposed to form an entity, treated as one letter.

    Then, the letters to be arranged are SGNTR (IAUE).

    These 6 letters can be arranged in 6P6 = 6 ! = 720 ways.

    The vowels in the group (IAUE) can be arranged amongst themselves in 4P4 = 4 ! = 24 ways.

    $$\therefore$$ Required number of words = (720 * 24) = 17280.

  9. In how many different ways can the letters of the word 'SOFTWARE' be arranged in such a way that the vowels always come together ?

      A. 120
      B. 360
      C. 1440
    D. 720

    Answer & Explanation

    Answer: Option D

    Explanation:

    The word 'SOFTWARE' contains 8 different letters.

    When the vowels OAE are always together, they can be supposed to form one letter.

    Thus, we hdve to arrange the letters SFTWR (OAE).

    Now, 5 letters can be arranged in 6 ! = 720 ways.

    The vowels (OAE) can be arranged among themselves in 3 ! = 6 ways.

    $$\therefore$$ Required number of ways = (720 * 6) = 4320.

  10. In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels ajways come together ?

      A. 120
      B. 720
    C. 4320
      D. 2160

    Answer & Explanation

    Answer: Option C

    Explanation:

    The word 'OPTICAL' contains 7 different letters.

    When the vowels OIA are always together, they can be supposed to form one letter.

    Then, we have to arrange the letters PTCL (OIA).

    Now, 5 letters can be arranged in 5 ! = 120 ways.

    The vowels (OIA) can be arranged among themselves in 3 ! = 6 ways.

    $$\therefore$$ Required number of ways = (120 * 6) = 720.

How many words can be formed from a letter SIGNATURE?

1 Answer. (e) The word SIGNATURE consists of nine letters comprising four vowels (A, E, I and U) and five consonants (G, N, R, T and S). When the four vowels are considered as one letter, we have six letters which can be arranged in 6P6 ways ie 6! ways.

How many words can be formed using letter SIGNATURE such that vowels come together?

The vowels in the group (IAUE) can be arranged amongst themselves in 4P4 = 4 ! = 24 ways. Required number of words = (720 * 24) = 17280.

How many 3 letter words can be formed from SIGNATURE if repetition of letters is not allowed?

If repetition is not allowed, we have 4 choices for the first letter, 3 choices for the second letter, and 2 choices for the third letter. Therefore, we can form 4*3*2 = 24 such “words".

How many 3 letter words can be formed out of the letters of the word SIGNATURE?

The word SIGNATURE has 9 different letters. The number of 3-letter words that can be formed = 3!

How many 3 letter words can be formed from SIGNATURE if repetition is not allowed?

=720. Hence, the no. of 3 letter words formed from the word LOGARITHMS without repetition is 720.

How many 3 letter words can be formed using Abcde if I repetition is not allowed II repetition is allowed?

(ii) When repetition of letters is allowed, each place can be filled by any of the 5 letters in 5 ways. ∴ the required number of ways =(5×5×5)=125. ∴ the required number of ways = ( 5 × 5 × 5 ) = 125 .

How many 3 letter words with or without meaning can be formed using the letters of the word flash?

So, the number of 3-letter words with or without meaning that can be formed using the letters of the word 'FLASH' is 60.

How many 3 letter words with or without meaning can be formed out of the letters of the word Monday when repetition of words is allowed?

Therefore, the number of words that can be formed using all the letters of the word MONDAY, using each letter exactly once is 6×5×4×3×2×1=6! =720.

How many 3 letter words can be formed using a b/c d/e if I repetition is not allowed II repetition is allowed?

So, the required number of 3-letter words =(5×4×3)=60.

How many 4 letter words can be formed using a b/c d and e if repetition of letters is allowed?

Solution : The number of different words that can be formed by using the four letters a,b,c,d, while the letter can be repeated is `4^4=256. ` Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

How many 3 letter words can be made if letters can be repeated?

ways to form a word with a repeated letter. Consequently, there are 24+18=42 distinguishable three letter words that can be formed with the letters of the word SERIES. Show activity on this post.

How many 3 letter words can be formed from the letters Abcde if letters can be repeated in a word?

If letters can be repeated as many times as you want, there are 6 options (A, B, C, D, E, or F) for the first letter, second letter, and third letter. Then 63=216 are the number of options for all three-letter-words.

How many words of 3 letters no repeat are there?

There are 15,600 different 3-letter passwords, with no letters repeating, that can be made using the letters a through z.

How many ways are there to form 3

Without any restrictions on the number of repetitions, we found 216 three-letter words.

How many three


`therefore " the required number of ways "=(5xx5xx5)=125. `

How many ways 4 letters can be formed from a b/c d/e and f if repetition is allowed?

possibilities in total. How many 4 letter words (string of letters) can be formed using the letters ABCDE if repetition is allowed? As repetition is allowed there are 5 possibilities (A, B, C, D, E ) for each letter in the word. So total number of words is : 5 * 5 * 5 * 5 = 5^4.