Ashley is packing her bags for her vacation. She has 7 unique socks, but only 3 fit in her bag. How many different groups of 3 socks c

Question

Ashley is packing her bags for her vacation. She has 7 unique socks, but only 3 fit in her bag.
How many different groups of 3 socks can she take?

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Madelyn 1 month 2021-10-15T18:00:56+00:00 1 Answer 0 views 0

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    2021-10-15T18:02:36+00:00

    Answer:

    There are 35 possible group of 3 socks from a total of 7

    Step-by-step explanation:

    Given

    Number of unique socks = 7

    Number of possible selection = 3

    Required

    Number of ways she can make her selection.

    The question can be categorised as combination; reason being that words like “take” as used in the question points to combination or selection.

    To solve this, we make use of combination formula.

    nCr = nPr/r!

    Where n = 7 and r = 3

    By substitution, we have

    7C3 = 7P3÷3!

    Taking it one at a time

    7P3 = 7!÷(7-3)!

    7P3 = 7! ÷ 4!

    7P3 = 7 * 6 * 5 * 4! ÷ 4!

    7P3 = 7 * 6 * 5

    7P3 = 210

    3! = 3 * 2 * 1

    3! = 6.

    So,

    7C3 = 210 ÷ 6

    7C3 = 35.

    Hence, there are 35 possible group of 3 socks from a total of 7

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45:7+7-4:2-5:5*4+35:2 =? ( )