Probability - Counting for 7

Probability Level 3

How many numbers in T = { 1 , 2 , 3 , . . . . , 100000 } T= \{1, 2, 3, ...., 100000\} whose sum of their digits is 7 7 ?

For example 142 ⟹ 1 + 4 + 2 = 7 142 \implies 1+4+2 = 7 and 31201 ⟹ 3 + 1 + 2 + 0 + 1 = 7 31201 \implies 3+1+2+0+1 = 7 are such numbers.


The answer is 330.

Pop Wong by Pop Wong , 47, Hong Kong

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1 solution

This is equivalent to finding the number on non-negative integer solutions to the equation a + b + c + d + e = 7, which is a ‘stars and bars’ equation with solution 11C7 = 330.

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