work Question 14, 11.8.35 HW Score: $$ 80 \% $$, 12 of 15 points Pointa: 0 of 1 How many different committees can be formed from 9 teachers and 36 ptudents if the committee consists of 4 teachers and 3 students? In how many ways can the committee of 7 members be selected? $$ \square $$

Question

UpStudy AI · Accepted Answer

**Step 1: Choose 4 Teachers from 9**

The number of ways to choose 4 teachers from 9 is given by the combination formula:
$$
\binom{9}{4} = \frac{9!}{4!(9-4)!} = \frac{9!}{4!5!} = 126.
$$

**Step 2: Choose 3 Students from 36**

Similarly, the number of ways to choose 3 students from 36 is:
$$
\binom{36}{3} = \frac{36!}{3!(36-3)!} = \frac{36 \times 35 \times 34}{3 \times 2 \times 1} = 7140.
$$

**Step 3: Form the Committee**

Since the choices are independent, multiply the two results together to find the total number of ways to form the committee:
$$
126 \times 7140 = 899640.
$$

Thus, the number of different committees of 7 members (4 teachers and 3 students) is:
$$
\boxed{899640}.
$$
There are 899,640 different ways to form the committee.

work
Question 14, 11.8.35
HW Score: , 12 of 15 points
Pointa: 0 of 1

How many different committees can be formed from 9 teachers and 36 ptudents if the committee consists of 4 teachers and 3 students?

In how many ways can the committee of 7 members be selected?

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work Question 14, 11.8.35 HW Score: , 12 of 15 points Pointa: 0 of 1 How many different committees can be formed from 9 teachers and 36 ptudents if the committee consists of 4 teachers and 3 students? In how many ways can the committee of 7 members be selected?