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

your answer is gonna be 56

some explanation stuff if needed :

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.

hope i helped :)

~ mo