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If n is an odd integer, what is the number of ways to choose three numbers from the set {1, 2, 3,..., n}?

1. 3(n − 1)/n(n − 2)
2. (3(n + 1)²)/(2n(n − 1)(n − 2))
3. (n − 2)/(n(n − 1))
4. 3(n − 1)/(2n(n − 2))

Correct answer: 3(n − 1)/(2n(n − 2))

Solution

The correct option is derived from the combinatorial formula for choosing 3 numbers from a set of n elements, adjusted for the specific case where n is an odd integer. It simplifies to the expression 3(n − 1)/(2n(n − 2), which accurately reflects the number of combinations possible under the given constraints.

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