Astore is selling 5 types of hard candies: cherry, strawberry, orange, lemon and pineapple. how many ways are there to choose: (a) 32 candies? (b) 32 candies with at least a piece of each flavor? (c) 32 candies with at least 4 cherry and at least 6 lemon?

The number of ways of selecting of n items form r different items =

A store is selling 5 types of hard candies: cherry, strawberry, orange, lemon and pineapple.

A) How many ways are there to choose 32 candies?

So, n = no. of items = 32

r = no. of types of items = 5

So, No. of ways to choose 32 candies =

                                                               =

                                                                 =

                                                                 =

So, No. of ways to choose 32 candies is 58905

B)32 candies with at least a piece of each flavor?

Out of 32 you choose 5 candies of different types

So, Remaining candies = 32 - 5 = 27

So, No. of ways to choose 27 candies =

                                                               =

                                                                 =

                                                                 =

So, No. of ways to choose 32 candies with at least a piece of each flavor is 31465

C) 32 candies with at least 4 cherry and at least 6 lemon?

So, you already choose 6+4= 10

So, remaining candies = 32-10 = 22

So, No. of ways to choose 22 candies =

                                                               =

                                                                 =

                                                                 =

Hence No. of ways to choose 32 candies with at least 4 cherry and at least 6 lemon is 14950

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