Question

For mr. fujimoto's class, there are 7 possible assignments. however, students only have to choose 5 assignments to complete and submit. if the order in which the students submit the assignments doesn't matter, how many different combinations of 5 are there?

Answer 1

we know that

The formula for combinations is
C=n!/[(n-r)!*r!]
where
n is the total number of objects you choose from
r is the number that you choose to arrange

in this problem
n=7 assignments

r=5 assignments

C=7!/[(7-5)!*5!]-----> C=7!/[2!*5!]---> (7*6*5!)/(2*5!)-----> C=21

the answer is

21