Emily Is Packing Her Bags For Her Vacation. She Has 6 Unique Faberg…

Emily is packing her bags for her vacation. She has 6 unique Fabergé eggs, but only 3 fit in her bag. How many different groups of 3 Fabergé eggs can she take?

Answer:

20

Step-by-step explanation:

Formula to use:

[tex]_{n} C_{r} = \frac{n!}{r!(n – r)!} [/tex]

n = 6

r = 3

[tex]_{n} C_{r} = \frac{6!}{3!(6 – 3)!} \\ \\ \: \: \: \: \: \: \: \: = \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1(3)!} \\ \\ \: \: \: \: \: \: \: \: = \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1(3 \times 2 \times 1)} \\ \\ \: \: \: \: \: \: \: \: = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} \\ \\ \: \: \: \: \: \: \: \: = \frac{120}{6} \\ \\ \: \: \: \: \: \: \: \: = 20[/tex]

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