Chapter 12.6, Problem 3STP

For Exercises 1-7, choose the correct letter.

There are 12 people on the basketball team. How many different starting lineups can be chosen?

A. 120 B. 792 C. 95,040

D. 3,991,680

To determine

Determine the value of the given statement.

Answer to Problem 3STP

B

Explanation of Solution

Given:

Given statement is :

There are 12 people on the basketball team . How many different 5-person starting lineups can be chosen

Formula Used:

  $C{}_r=\frac{n!}{r!(n-r)!}$

Calculation:

Since we need to choose 5 people from 12 without replacement and order of players in the lineup does not matter, so, the number of different 5-person lineups =

  $C{}_5=\frac{12!}{5!(12-5)!}=\frac{12!}{5!7!}=\frac{12\cdot 11\cdot 10\cdot 9\cdot 8}{5\cdot 4\cdot 3\cdot 2}=12\cdot 11\cdot 3\cdot 2=792$

So, the correct option is B.