permutations and combinations

Question

Your history teacher gives you a list of eight study questions. Five of the eight will be on the next test. How many different combinations of eight can the teacher choose from the eight study questions?

Answer 1

8 questions, and your teacher will choose 5. The order doesn’t matter just whether or not they’re on the test!

Thats a combination (permutation is where the order matters).

nCr= ^(n!)/_(n-r)!·r!

n is the number of options

r is the number you choose

! is “factorial” (multiplying every whole number down the 1; ex: 4! = 4·3·2·1 = 24)

so lets substitute:

n= 8 questions from which to choose

r= 5 the number the teacher will choose

₈C₅= ^(8!)/_(8-5)!·5!

= ^(8!)/_(3)!·5!

= ^{(8·7·6·5·4·3·2·1)}/_{(3·2·1)·(5·4·3·2·1)}

= ^40,320/_(6)·(120)

= ^40,320/₇₂₀

_{= 56}

There are 56 possible combinations of 5 questions your history teacher could choose.