Probability If the student council consists of five seniors

Probability

If the student council consists of five seniors and five juniors, how many ways are there to choose a delegation and a speaker so that the delegation has at least one senior and at least one junior? (The speaker can be a senior or a junior.)

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Solution

The speaker can be a senior or a junior. We have to choose 2 students among 10 avalible. And the selection must pass the criteria one among five juniors and other among five seniors.

No. ways are there to choose a delegation and a speaker = 5 C 1 * 5 C 1

Total Possibilties are = 10 C 2

Probability of choosing a delegation and a speaker so that the delegation has at least one senior and at least one junior = 5 C 1 * 5 C 1 / 10 C 2 = nCr(5,1)*nCr(5,1)/nCr(10,2) = 0.556