Question

A combinatorics problem to get a classroom ready. Show all your work.

a. I have 60 students and I'm going to give each one a single gumdrop. One is all you need. There are 6 flavors. How many possible ways can the students get their sugary candy?

b. I have 16 identical white teacups. I hate white teacups! I am going to paint them. I can paint each one Ivory, Cream, Eggshell, Lace, Bone, or Vanilla. How many ways are there to do this?

c. I have 10 different tasks on my to do list. In how many orders can I choose to do them?

Answer 1

a)

total students=60

total flavors=6

it is a combination problem,order doen not matter here

so, total possible ways can the students get their sugary candy = 60C6 = 60!/(6!*54!) = 50063860

b)

total cups=16

total colors=6

total posssible ways to do this = 16C6 = 8008

c)

total different tasks = 10

total orders can choose to do them = 10! = 3628800

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please revert if have any doubts