How many 4-letter words with or without meaning, can be formed out of LOGARITHMS
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The correct option is A 720 Step 1: Use combination formula In the word LOGARITHMS there are 10 unique letters which are, A,G,H,I,L,M,O,R,Sand T. Now we must create a three-letter word with or without meaning, with the restriction that letter repetition is not permitted, i.e., we cannot use the same letter more than once to create three-letter words. We know that number of combinations of r objects chosen from n objects when repetition is not allowed is given by Crn=n!r!(n-r)! where n! is n!=n×(n–1)×(n–2)×(n–3)×……..×3×2×1 So, three letters out of 10 unique letters can be selected in C310ways. By using the above formula we get C 310=10!3!(10-3)! =10!3!(7) ! Step 2: Calculate the number of 3-letter words In general, n! can be used to arrange n distinct objects. We chose three letters from a list of ten unique letters, and these letters can be put in three different ways. Total number of 3 letter word =C310×3! ∴ C310×3!=10!3!(7)!×3! =10 !7! =10×9×8×7!7! =10×9 ×8 =720 Hence, the word LOGARITHMS if repetition of letters is not allowed can form 720 number of 3-letter words. A. 40 B. 400 C. 5040 D. 2520 E. None of these Solution(By Examveda Team) 'LOGARITHMS' contains 10 different letters. How many 4So, the total arrangement is given by, 10×9×8×7=5040 .
How many 4Explanation: 'LOGARITHMS' contains 10 different letters. = Number of arrangements of 10 letters, taking 4 at a time. = 5040.
How many words can be formed from LOGARITHMS?Hence, the no. of 3 letter words formed from the word LOGARITHMS without repetition is 720. Hence the correct option of this question is option (a).
How many 4 letters words with or without meaning can be formed out of the letters of the word signature if repetition of the letters is not allowed?Hence, the answer is 5040. Was this answer helpful?
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