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
Hi, Here is my approach. We need to find the sum of digits equal to 5 for all numbers upto 9999.
Unique combinations are as follows:
1) 5,0,0,0
2) 4,1,0,0
3) 3,2,0,0
4) 3,1,1,0
5) 2,2,1,0
6) 1,1,1,2
Since the problem asks for all numbers less than 9999, we need to include single,double,three and four digit numbers.
Now it becomes a permutation problem.
1) Thousand place can be filled with 4 digits, hundreds with any of the remaining 3 and so on. And since there are three zeros, there are duplications. So divide by 3!. i.e. 4!/3! = 4
2) 4!/2! = 12
3) 4!/2! = 12
4) 4!/2! = 12
5) 4!/2! = 12
6) 4!/3! = 4.
Adding all the above IMO, C-> 56.
Please post the OA.
