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17 June, 03:03

Diego's doctor has recommended that his daily diet should include 3 vegetables, 2 fruits, and 2 whole grains. At the grocery store, Diego has a choice of 9 vegetables, 9 fruits, and 11 whole grains. In how many ways can he get his daily requirements if he doesn't like to eat 2 servings of the same thing in 1 day

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  1. 17 June, 03:48
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    166320 ways

    Step-by-step explanation:

    In this case we must calculate the number of combinations for each option, and then multiply the result of each one, like this:

    Number of ways you can choose 3 vegetables out of 9 available:

    nCr = n! / (r! * (n-r) !)

    in this case n = 9, r = 3, replacing:

    9C3 = 9! / (3! * (9-3) !) = 84

    Number of ways you can choose 2 fruits out of 9 available:

    9C2 = 9! / (2! * (9-2) !) = 36

    Number of ways you can choose 2 whole grains out of 11 available:

    11C2 = 11! / (2! * (11-2) !) = 55

    So according to the rule of the products how many ways you can choose the daily diet

    84*36*55 = 166320
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