How many even 4 digit whole numbers are there if repetition is not allowed?
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How many 5 digit even numbers can be made if: repetition is not allowed and 4 must be included. Use the indirect method to do this: So basically i believe , you have to find the # of ways, 5 digit even #s that can be made, then subtract it from even numbers that do not include 4. but i don't know how to act on my plan, how can i find how many 5 digit even numbers
there are. and how can i find the number of ways that do not include 4 , but are even numbers?
grapz said: How many 5 digit even numbers can be made if: repetition is not allowed and 4 must be included. The first question is what is considered a five digit number? Is 4=00004 considered such a number? If so the answer is \(\displaystyle \left( 5 \right)\left( {10^4 } \right)\). If the first digit must be at least 1,
example 10400, then the answer is \(\displaystyle \left( {10^4 } \right) + \left( 8 \right)\left( 4 \right)\left( {10^3 } \right)\).
hm the defination of a 5 digit number in this case would be for the first number to be at least one. but, repetition is not allowed. i believe the method u shown here allows repetition.
grapz said: a 5 digit number in this case would be for the first number to be at least one. but, repetition is not allowed. In that case the answer is \(\displaystyle \left( 9 \right)\left( 8 \right)\left( 7 \right)\left( 6 \right) + \left( 8 \right)\left( 4 \right)\left( 8 \right)\left( 7 \right)\left( 6 \right)\). Count
those beginning with a 4 and add those that do not.
thanks. So this is now what i did. The question was, how many 5 digit even numbers can be made if repetition is not allowed and the number four must be included. so i did 8 x 8 x 7 x 6 x 4 - 7 x 7 x 6 x 5 x 3 = 6342. but the answer is 7686. 8x8x7x6x4- thats the number of 5 digit even numbers, with no repetition. and 7x7x6x5x3 is when 4 is excluded.
pkaElite Member
grapz said: The question was, how many 5 digit even numbers can be made if repetition is not allowed and the number four must be included. Are you saying that the answer is 7686? There are 3024 five-digit numbers that begin with
the digit 4 with no repetition. Re: There are how many 4-digit even numbers if the first digit cannot be a [#permalink]
Bunuel wrote: There are how many 4-digit even numbers if the first digit cannot be a zero? A. 3,600 Hi, FIRST, lets write down the restrictions 1) these are four digit even numbers, so first digit can be 1 to 9, and the units digit can be 2,4,6,8, or 0.. Now, lets work out a solution on these restrictions 1) units digit= any of five even digits.. 0,2,4,6,8.. the ways= 5*10*10*9= 4500 another way 1) what are the different ways without any restriction =10*10*10*10=10,000.. ans C How many even 4 digit numbers are there if repetition is not allowed?Hence, there are 48 four digit even numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated.
How many odd numbers of four digits are there no repetition of digits?So the number of four-digit odd numbers can be formed is 2240.
How many even 4 digit whole numbers are there?Together, this gives 2,296 numbers with 4 distinct digits that are even.
How many 4 digit numbers are there if any digits can be repeated?So, the required number of numbers =(9×10×10×10)=9000.
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