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
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
...




