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13 May, 04:05

7. The manager of the soda shop decides that because you are a good customer, you may use a flavor as many times as you'd like. How many different possible mixtures can you make now (remember, you have 13 flavors available to you and you must choose 6?

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  1. 13 May, 05:00
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    The different possible mixtures can you make is 1716.

    Step-by-step explanation:

    Given that,

    The total number of flavors available in the shop = 13 flavors The number of flavors you need to choose = 6 flavors

    Here, we have to use the formula for combination,

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

    where,

    n is the total number of flavors r is the number of flavors you need to choose

    ⇒ 13C6 = 13! / 6! * (13-6) !

    ⇒ 13! / (6! * 7!)

    ⇒ 13 * 12 * 11 * 10 * 9 * 8 * 7! / (6! * 7!)

    ⇒ 13 * 12 * 11 * 10 * 9 * 8 / 6!

    ⇒ 13 * 12 * 11 * 10 * 9 * 8 / 6 * 5 * 4 * 3 * 2 * 1

    ⇒ 1716

    Therefore, you can 1716 different possible mixtures.
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