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31 October, 23:11

11. A basketball team of 16 players consists of 6 guards, 7 forwards, and 3 centers. The coach decides to randomly select 5 players to start the game. What is the probability of 2 guards,

2 forwards, and 1 center starting the game?

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  1. 1 November, 02:59
    0
    0.2163

    Step-by-step explanation:

    Firstly, we need to evaluate the total number of possible outcomes. Since there are 16 players, and we are selecting just 5, the total number of possibilities is 16C5 = 4,368

    Now, we know we need 2 guards from 6, 2 forwards from 7 and 1 center from 3 to start the game. Since we are selecting, it is a combination problem. These can be done in the following number of ways:

    6C2 * 7C2 * 3C1

    The probability is thus (6C2 * 7C2 * 3C1) / 16C5 = 945/4368 = 0.2163
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