Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 11 - Probability and Statistics - 11-1 Permutations and Combinations - Lesson Check: 3

Answer

$10$ possible combinations.

Work Step by Step

Using the formula for combinations, $\frac{n!}{r!(n-r)!}$, where $n =$ the size of the set, and $r=$ the size of the combinations. $n = 5$, and $r = 2$ Substitute these values for $n$ and $r$ in the formula: $\frac{5!}{2!(5-2)!}$ Simplify the dominator: $=\frac{5!}{2! \times 3!}$ Expand the factorials: $=\frac{5\times 4 \times 3 \times2 \times 1}{2 \times 1 \times 3 \times2 \times 1}$ Calculate: $\frac{120}{12} = 120 \div 12 = 10$ There are $10$ possible combinations.
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