Question

 

There are 10 ice creams. There are strawberry, coconut, matcha, and melon flavor. Suppose that each ice cream of the same flavor is indistinguishable from another.

a. How many combinations are there such that there is at least 2 strawberry and at most 2 coconut ice cream?

b. How many combinations are there such that there is at least 2 strawberry, at most 2 coconut ice cream, and at least 1 matcha if someone 3 ice creams. (Hint: There is now 7 ice cream left?)

Answer 1

a)

Its a ball and bin problem setup where the ice creams are the balls and the flavours are the bins.

Let be the flavoured ice cream,i =strawberry,coconut,matcha,melon

Our problem : Find possible combinations such that

Possible combinations such that

is

Possible combinations such that

is

Possible combinations such that is (*) -(**) 165-56=109

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If we assume there are atleast one ice cream of each kind ,then

Our problem : Find possible combinations such that

Possible combinations such that

is

Possible combinations such that

is

Possible combinations such that is (i) -(ii) 56-20=36

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b)

Our problem : Find possible combinations such that

Possible combinations such that

is

Possible combinations such that

is

Possible combinations such that is (iii) -(iv) 35-4=31