How many positive integer less than 10000 are there in which the sum of digits is 5
(A) 31 (B) 51(C) 56(D) 62(E) 934.
(A) 31 (B) 51(C) 56(D) 62(E) 934.
We will keep our upper barrier as 9,999 inclusive. I prefer doing it this way.
Now, if the sum of digits have to add up to 5 we have the following options
0005 which can be arranged in 4!/3!=4 Ways
2003 which can be arranged in 4!/2!=12 Ways
1130 which can be arranged in 4!/2!=12 Ways
4100 which can be arranged in 4!/2!=12 ways
1121 which can be arranged in 4!/3!=4 Ways
2210 which can be arranged in 4!/2!=12 Ways
Summing up we get 56 ways. Hence[spoiler] C[/spoiler]
