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How many ways can a committee chairman choose 4 people for a subcommittee if there are 12 members on the whole committee?
a. 48
b. 495
c. 11,880
d. 20,736

Respuesta :

naǫ
A group of k elements can be chosen from a group of n elements in [tex]\frac{n!}{k!(n-k)!}[/tex] ways.

[tex](^{12} _4)=\frac{12!}{4!(12-4)!}=\frac{12!}{4! \times 8!}=\frac{8! \times 9 \times 10 \times 11 \times 12}{2 \times 3 \times 4 \times 8!}=\frac{9 \times 10 \times 11 \times 12}{2 \times 3 \times 4}= \\ \\ =3 \times 5 \times 11 \times 3=495[/tex]

The answer is B. 495.

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