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

Answer 1

The sum of the digits is to be 5. So the possibilities are :

3 ZEROES and a 5,   we have ⁴P₁  as in  0005,0050,0500,5000 thus 4 integers.

1 One and one 4, we have ⁴P₂ possibilities  (like 0014, 0104.....) thus 12 integers

2 One's and a 3, we have (⁴P₃/2!) (the 2 1's are identical) thus 12 integers.

One 2 and one 3 …. again 12 integers.

3 one's and a 2                4 integers.

1 One and 2 Two's           12 integers 

Total of 56 such integers.

 

Pradip