Respuesta :
Answer:
The number of ways of selecting of n items form r different items =[tex]^{(n+r-1)}C_{(r-1)}[/tex]
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 = [tex]^{(32+5-1)}C_{(5-1)}[/tex]
= [tex]^{36}C_{4}[/tex]
= [tex]\frac{36!}{4!(36-4)!}[/tex]
= [tex]58905[/tex]
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 = [tex]^{(27+5-1)}C_{(5-1)}[/tex]
= [tex]^{31}C_{4}[/tex]
= [tex]\frac{31!}{4!(31-4)!}[/tex]
= [tex]31465[/tex]
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 = [tex]^{(22+5-1)}C_{(5-1)}[/tex]
= [tex]^{26}C_{4}[/tex]
= [tex]\frac{26!}{4!(26-4)!}[/tex]
= [tex]14950[/tex]
Hence No. of ways to choose 32 candies with at least 4 cherry and at least 6 lemon is 14950
