Use the Combinations Formula
Use the formula for
$$\mathrm { n } ^ { \mathrm { C } _ { \mathrm { r } } }$$ to evaluate the expression.
-Ron finds 9 books at a bookstore that he would like to buy, but he can afford only 5 of them. In how many ways can he make his selection? How many ways can he make his selection if he decides that one of the
Books is a must?
A)126; 70
B)15,120; 1680
C)3024; 1680
D)7560; 840 5 Additional Concepts
Evaluate the expression.

Question

Use the Combinations Formula
Use the formula for
 $$\mathrm { n } ^ { \mathrm { C } _ { \mathrm { r } } }$$ to evaluate the expression.
-Ron finds 9 books at a bookstore that he would like to buy, but he can afford only 5 of them. In how many ways can he make his selection? How many ways can he make his selection if he decides that one of the
Books is a must?
A)126; 70
B)15,120; 1680
C)3024; 1680
D)7560; 840 5 Additional Concepts
Evaluate the expression.

Quizplus · Accepted Answer

The number of ways Ron can choose 5 books out of 9 is calculated using the combination formula $\mathrm{nC}_\mathrm{r} = \frac{n!}{r!(n-r)!}$, where $n$ is the total number of items, $r$ is the number of items to choose, and "!" denotes factorial. For the first part, $n=9$ and $r=5$, so the calculation is $\frac{9!}{5!(9-5)!} = \frac{9!}{5!4!} = 126$. If one book is a must, then Ron is actually choosing 4 out of the remaining 8 books, so the calculation is $\frac{8!}{4!(8-4)!} = \frac{8!}{4!4!} = 70$.

Use the Combinations Formula Use the Formula For nCr\mathrm { n } ^ { \mathrm { C } _ { \mathrm { r } } }nCr​

Use the Combinations Formula
Use the Formula For $\mathrm { n } ^ { \mathrm { C } _ { \mathrm { r } } }$