Question

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12b: applications with probability
score: 4/9 answered: 4/9
question 5
in how many ways can 2 books be chosen from a group of nine?
your answer is :
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Explanation:

Step1: Recall combination formula

The combination formula is $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n$ is the total number of items and $r$ is the number of items to be chosen. Here $n = 9$ and $r=2$.

Step2: Calculate factorial values

$n!=9! = 9\times8\times7\times6\times5\times4\times3\times2\times1$, $r!=2!=2\times1$, and $(n - r)!=(9 - 2)!=7!=7\times6\times5\times4\times3\times2\times1$. Then $C(9,2)=\frac{9!}{2!(9 - 2)!}=\frac{9\times8\times7!}{2\times1\times7!}$.

Step3: Simplify the expression

Cancel out the $7!$ terms. We get $C(9,2)=\frac{9\times8}{2\times1}=\frac{72}{2}=36$.

Answer:

36