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Problem Solving (PS) | Re: How many positive integers less than 10,000 are there in

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Bunuel wrote:

zaarathelab wrote:
How many positive integers less than 10,000 are there in which the sum of the digits equals 5?

A) 31
B) 51
C) 56
D) 62
E) 93


Consider this: we have 5\(d\) 's and 3 separators\(|\) , like:\(ddddd|||\) . How many permutations (arrangements) of these symbols are possible? Total of 8 symbols (5+3=8), out of which 5\(d\) 's and 3\(|\) 's are identical, so\(\frac{8!}{5!3!}=56\) .

With these permutations we'll get combinations like:\(|dd|d|dd\) this would be 3 digit number 212 OR\(|||ddddd\) this would be single digit number
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