The product of three numbers will equal ‘0’ if

at least one of the numbers is zero. Another way is to substract a number of combinations when none of the numbers equal zero from a total number of combinations.

A total number of combinations of 3 balls out of 6 is 6C3=20. The number of combinations of all ones is 3C3=1. Thus, the number of combinations of none zero out of three is 20-1=19.

Double check the longer way (

at least)

Number of combinations of exactly one zero (two '1'): 3C1*3C2=9

Number of combinations of exactly two zeros (one '1'): 3C2*3C1=9

Number of combinations of exactly tree zeros: 3C3=1

Add them all up and the answer is 19.

- Stolyar?

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Respect,

KL