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Answer:
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