math help pls! (prob. distribution) ?

The probability that exactly two students will be selected when five people are selected from five students and four teachers

is...?

 Explain.

2 Answers

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  • 1 month ago

    Let's count the ways to get exactly 2 students (and 3 teachers).

    From the 5 students, pick 2:

    C(5,2) = (5 * 4) / (2 * 1) = 10 ways

    From the 4 teachers, pick 3:

    C(4,3) = (4 * 3 * 2) / (3 * 2 * 1) = 4 ways

    Multiply to get the total ways of picking exactly 2 students:

    10 * 4 = 40

    So there are 40 ways to get the desired outcome of exactly 2 students.

    Now just take all 9 people and pick any 5 of them.

    C(9,5) = (9 * 8 * 7 * 6 * 5) / (5 * 4 * 3 * 2 * 1)

    = 126 ways

    Divide to get the probability:

    40/126

    = 20/63

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  • p = (4C3 *5C2) / (9C5)

    p = (40)/(126)

    p = 20 / 63

    I'm just lazy when I say this, but you should keep on trying questions until you see the pattern. Having everything taught to you makes you develop a systemic approach to math instead of inquiry-based

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