Michael Is Packing His Bags For His Vacation. He Has 6 Unique Books, But O…

Michael is packing his bags for his vacation. He has 6 unique books, but only 4 fit in his bag. How many different groups of 4 books can he take?

Answer:

15

Step-by-step explanation:

Formula:

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

n = 6

r = 4

[tex]_{n} C_{r} = \frac{6!}{4!(6 – 4)!} \\ \\ \: \: \: \: \: \: \: \: = \frac{6!}{4!(2)!} \\ \\ \: \: \: \: \: \: \: \: = \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1(2 \times 1)} \\ \\ \: \: \: \: \: \: \: \: = \frac{6 \times 5 \times 4 \times 3}{4 \times 3 \times 2 \times 1} \\ \\ \: \: \: \: \: \: \: \: = \frac{360}{24} \\ \\ \: \: \: \: \: \: \: \: = 15[/tex]

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