How many ways are there to choose five doughnuts if there are eight varieties (and only the type of each doughnut matters)?

There are 56 ways to choose 5 from 8 varieties.

Step-by-step explanation:

a) Choosing 5 out of 8

This is a combination problem, given by the formula below:

C(n,r)=?

C(n,r)=C(8,5)

=8!/(5!(8−5)!)

= 56

b) A combination is the number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed. The result of this combination of 5 out of 8 varieties shows that there 56 ways one can choose.  The formula is given by 8 factorial divided by (5 factorial by 3 factorial).

aloha~! my name is zalgo and i am here to you out on this amazing day. to answer your question, yes, nonzero numbers can have a greatest common factor and that would be 1. still don't get it? let me considering every number is divisible by 1 and hence every number has 1 as a factor of theirs. so, if 2 nonzero numbers didn't share any gcf (greatest common factor), they would still have a factor in common and that would be 1.

i hope that this ! : p

"stay and stay proud! " - zalgo

(by the way, do you mind marking me as brainliest? i'd greatly appreciate it! mahalo! x3)