SOLUTION: In how many ways can a group of 4 students and a teacher be chosen from 12 students and 4 teachers?

Question 1067726: In how many ways can a group of 4 students and a teacher be chosen from 12 students and 4 teachers?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you've got 12 students and 4 teachers.
you want to choose 4 students and 1 teacher.

the students can be chosen in c(12,4) ways.
the teacher can be chosen in c(4,1) ways.
they can both be chosen in c(12,4) * c(4,1) ways.

c(12,4) = 12! / (4! * 8!) = 495
c(4,1) = 4! / (1! * 3!) = 4
495 * 4 = 1980

they can both be chosen in 1980 ways.

to see how it works, make it real simple.
assume 3 students and 2 teacher.
you want 2 students and 1 teacher.

per the formula, this can ocurr in c(3,2) * c(2,1) ways which is equal to 6 ways.

let the students be a,b,c
let the teachers be 1,2

you want 2 students and 1 teacher.

the number of ways will be:

a,b,1
a,b,2
a,c,1
a,c,2
b,c,1
b,c,2

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