Question

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).?

Answer 1

Answer:

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 2

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