# Permutations and Restrictions

Can you check my answers and help me with B?

Preparing a plate of cookies for 8 children, 3 types cookies {chocolate chip, peanut butter, oatmeal}, unlimited amount of cookies in supply but only cookie per child.

One cookie per plate, one plate per child.

A) How many different plates can be prepared? C(8,3) = 56

B) How many different plates can be prepared if at least one of each kind of cookie is given out ?

C) How many different plates can be prepared if no one likes oatmeal? C(8,2) = 28

D) How many different plates can be prepared if two children need to get peanut butter? C(6,3) = + C(2,1) = 22

E) How many different plates can be prepared if the dog got into the kitchen and three are only two chocolate chip cookies left? C(6,2) + 2 = 17

https://brainmass.com/math/combinatorics/permutations-restrictions-21748

#### Solution Preview

I would suggest that instead of relying on the formulas for Combination try to actually count the possible combinations.

If we write the number of chocolate ...

#### Solution Summary

A step-by step solution that also visualizes the results. The different plates are given.