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