Question

How many 5 digit numbers are there whose digits sum to 39?

Answer 1

I would have to say 15 total ways

Answer 2

The distribution of the possible digits of the numbers are
1.) 9, 9, 9, 9, 3  [Number of arrangements = 5! / 4! = 120 / 24 = 5]
2.) 9, 9, 9, 8, 4  [Number of arrangements = 5! / 3! = 120 / 6 = 20]
3.) 9, 9, 9, 7, 5  [Number of arrangements = 5! / 3! = 120 / 6 = 20]
4.) 9, 9, 9, 6, 6  [Number of arrangements = 5! / (3! x 2!) = 120 / 12 = 10]
5.) 9, 9, 8, 8, 5  [Number of arrangements = 5! / (2! x 2!) = 120 / 4 = 30]
6.) 9, 9, 8, 7, 6  [Number of arrangements = 5! / 2! = 120 / 2 = 60]
7.) 9, 9, 7, 7, 7  [Number of arrangements = 5! / (3! x 2!) = 120 / 12 = 10]
8.) 9, 8, 8. 8, 6  [Number of arrangements = 5! / 3! = 120 / 6 = 20]
9.) 9, 8, 8, 7, 7  [Number of arrangements = 5! / (2! x 2!) = 120 / 4 = 30]
10.) 8, 8, 8, 8, 7  [Number of arrangements = 5! / 4! = 120 / 24 = 5]

Number of 5 digit numbers whose digit sum up to 39 = 5 + 20 + 20 + 10 + 30 + 60 + 10 + 20 + 30 + 5 = 210