Studdy AI Logo
Math

QuestionHow many ways can you form a committee of 3 teachers and 4 students from 9 teachers and 43 students?

Studdy Solution

STEP 1

Assumptions1. The total number of teachers is9. The total number of students is433. The committee consists of3 teachers and4 students4. Each committee member is distinct and can only be counted once

STEP 2

We need to find the number of ways to select teachers from9. This is a combination problem, as the order of selection does not matter. The formula for combinations isC(n,k)=n!k!(n−k)!C(n, k) = \frac{n!}{k!(n-k)!}where n is the total number of items, k is the number of items to choose, and ! denotes factorial.

STEP 3

Plug in the values for n and k to calculate the number of ways to select the teachers.
C(9,3)=9!3!(9−3)!C(9,3) = \frac{9!}{3!(9-3)!}

STEP 4

Calculate the number of ways to select the teachers.
C(9,3)=9!3!6!=84C(9,3) = \frac{9!}{3!6!} =84

STEP 5

Next, we need to find the number of ways to select4 students from43. This is also a combination problem.

STEP 6

Plug in the values for n and k to calculate the number of ways to select the students.
C(43,4)=43!4!(43−4)!C(43,4) = \frac{43!}{4!(43-4)!}

STEP 7

Calculate the number of ways to select the students.
C(43,4)=43!4!39!=123,410C(43,4) = \frac{43!}{4!39!} =123,410

STEP 8

Finally, to find the total number of ways to form the committee, we multiply the number of ways to select the teachers by the number of ways to select the students.
Total ways=C(,3)timesC(43,4)Total\, ways = C(,3) \\times C(43,4)

STEP 9

Plug in the values for C(9,3) and C(43,4) to calculate the total number of ways to form the committee.
Total ways=84times123,410Total\, ways =84 \\times123,410

STEP 10

Calculate the total number of ways to form the committee.
Total ways=84times123,410=10,366,440Total\, ways =84 \\times123,410 =10,366,440There are10,366,440 different ways to form the committee.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord