Perms and Combs (1 Viewer)

[potatoe456]

If a committee of 6 members is chosen from 4 teachers and 6 students, what is the probability that it contains 2 teachers and 4 students.

Can someone please explain to me why we have to divide the answer by 10C6??

 

[leclerc16]

because your answer has to be divided by the total possibilities of 6 members being chosen from 10 people, hence 10C6.

 

[liamkk112]

If a committee of 6 members is chosen from 4 teachers and 6 students, what is the probability that it contains 2 teachers and 4 students.

Can someone please explain to me why we have to divide the answer by 10C6??

in informal terms,
P(some specific event) = # of ways to get specific event / total # of ways without any restrictions

now the total # of ways without any restrictions to choose a committee of 6 members, given 10 candidates (4 teachers + 6 students), is 10C6
and the specific event we want is when the committee has 2 teachers and 4 students; there are 4C2 x 6C4 ways to do this

so using our formula above, P(committee has 2 teachers and 4 students) = (4C2 x 6C4) / 10C6

 

[potatoe456]

in informal terms,
P(some specific event) = # of ways to get specific event / total # of ways without any restrictions

now the total # of ways without any restrictions to choose a committee of 6 members, given 10 candidates (4 teachers + 6 students), is 10C6
and the specific event we want is when the committee has 2 teachers and 4 students; there are 4C2 x 6C4 ways to do this

so using our formula above, P(committee has 2 teachers and 4 students) = (4C2 x 6C4) / 10C6

tysm!