How many different ways are there to select 24 donuts if there are 7 types of donuts available (and donuts are only distinguished by their type).?

593,775 ways

Step-by-step explanation:

24 donuts have to be selected from 7 different varieties of donuts

n = 7

r = 24

Repetition is allowed

C (n+r-1, r) = C (7 + 24 - 1, 24)

= C (30,24)

Recall that C (n, r) = n! / (n-r) ! r!

C (30,24) = 30! / (30 - 24) ! 24!

= 30! / (6!24!)

= 593,775 ways

Answer: 346,789 ways

Step-by-step explanation:

Using the formular for permutation to calculate:

P = n!/r! (n-r) !

We need to select 24 apples from 7 types of apples

n=24, r=7

Permutation = 24!/7! (24-7) !

Permutation = 6.2*10^23/1.793*10^18

P = 346,789 ways