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 3 ice creams melted. (Hint: There is now 7 ice cream left.)

Answer 1

Total ice creams=10

(a)

Number of possible ice creams of each flavor

strawberry flavor.	2	3	4	5	6	7	8	9	10
coconut flavor.	0	1	2
matcha flavor.	0	1	2	3	4	5	6	7	8	9	10
melon flavor.	0	1	2	3	4	5	6	7	8	9	10

Total number of possible combination =(9+8+7)+(8+7+6)+(7+6+5)+(6+5+4)+(5+4+3)+(4+3+2)+(3+2+1)+(2+1+0)+(1+0+0)=109

(b)

3 ice creams melted.

Now total ice creams=7

strawberry flavor.	2	3	4	5	6	7
matcha flavor.	1	2	3	4	5	6	7
coconut flavor.	0	1	2
melon flavor.	0	1	2	3	4	5	6	7

Total number of possible combination = (3+3+3+2+1)+(3+3+2+1)+(3+2+1)+(2+1)+(1)=31