Question

question 8 of 10 there are 9 students in a class. the teacher chooses 2 students to go to the library. the order in which they are chosen does not matter. how many ways are there to choose the students? a. 72 b. 504 c. 81 d. 36

Explanation:

Answer:

D. 36

To determine the number of ways to choose 2 students out of 9 when order does not matter, we use the combination formula \( C(n, k)=\frac{n!}{k!(n - k)!} \), where \( n = 9 \) and \( k=2 \).

\[

$$\begin{align*} C(9,2)&=\frac{9!}{2!(9 - 2)!}\\ &=\frac{9!}{2!7!}\\ &=\frac{9\times8\times7!}{2\times1\times7!}\\ &=\frac{9\times8}{2\times1}\\ &=\frac{72}{2}\\ & = 36 \end{align*}$$

\]