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

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