Jessica Is Packing Her Bags For Her Vacation. She Has 999 Unique Fa…

Jessica is packing her bags for her vacation. She has 999 unique Fabergé eggs, but only 333 fit in her bag.

How many different groups of 333 Fabergé eggs can she take?

Answer:

84

Step-by-step explanation:

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

n = 9

r = 3

[tex]_{9}C _{3} = \frac{9!}{3!(9 – 3)!} \\ \\ \: \: \: \: \: \: \: \: = \frac{9!}{3!(6)!} \\ \\ \: \: \: \: \: \: \: \: = \frac{9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1(6 \times 5 \times 4 \times 3 \times 2 \times 1)} \\ \\ \: \: \: \: \: \: \: \: = \frac{9 \times 8 \times 7}{3 \times 2 \times 1} \\ \\ \: \: \: \: \: \: \: \: = \frac{504}{6} \\ \\ \: \: \: \: \: \: \: \: = 84[/tex]

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