Question

Jeanine Baker makes floral arrangements. She has 11 different cut flowers and plans to use 5 of them. How many different selections of the 5 flowers are possible?

Answer 1

She has 11 different cut flowers and plans to use 5 of them.

$\begin{gathered} ^nC_r\text{ = }\frac{n!}{(n-r)!\times r!} \\ \end{gathered}$

Here, 5 selections are made out of 11 .

$\begin{gathered} n\text{ = 11} \\ r\text{ = 5} \end{gathered}$

Substituting the values in the formula,

$\begin{gathered} ^{11}C_5\text{ = }\frac{11!}{(11-5)!\times5!} \\ ^{11}C_5\text{ = }\frac{11!}{6!\text{ }\times\text{ 5!}} \\ ^{11}C_5\text{ = }462 \end{gathered}$

Thus there are 462 selections possible .