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
OA C
(A) 31
(B) 51
(C) 56
(D) 62
(E) 93
OA C
the sum of the digits can be five
in the following cases
when the digits of the number are from the following sets
1. (0,0,0,5)
2.(1,0,0,4)
3.(1,2,2,0)
4.(3,2,0,0)
5.(3,1,1,0)
6.(2,1,1,1)
from set one the no. of digits with sum 5 = 4!/3!=4
from set two the no. of digits with sum 5 = 4!/2!=12
from set three the no. of digits with sum 5 = 4!/2!=12
from set four the no. of digits with sum 5 = 4!/2!=12
from set five the no. of digits with sum 5 = 4!/2!=12
from set six the no. of digits with sum 5 = 4!/3!=4
Therefore, the answer is 4 +12+12+12+12+4=56
OA C
