## Question

Three integers are chosen at random without replacement from the first 20 integers. The probability that their product is even 2/19.

### Solution

17/19

The product of any number of integers will be even if and only if at least one of the integers involved is even. Let *A* denote the event that the product of the three integers is even. Then *A*’ denotes the event that the product of three integers is odd. The total number of ways of choosing three integers out of 1, 2,…,20 is . The number of ways favourable to*A*’ is

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