Question 1077486: COMOBINATION
a jar contains 25 candies of which 15 are chocolate and 10 are mint. a sample of 5 candies is to be selected
a) how many different samples are possible?
b)how many samples contain chocolate candies?
c)how many sample contain 3 chocolate and 2 mint?
d)how many samples contain at least 4 mint candies?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 25C5 are the number of different samples=53130. ANSWER A
For chocolate, one way to look at samples that contain 5 is
probability of first is 15/25, then 14/24, then 13/23, then 12/22, then 11/21=0.0565... probability . Without rounding, multiply that by the 53130, and you get 3003.
This is 15C5, the number of ways you can choose 5 chocolates from 15 of them.
For chocolate candies,
15C5+15C4*10C1+15C3*10C2+15C2*10C1*15C1*10C4
Using that last approach, then 4 chocolates is 15C4*10C1, because one has to be a mint and there are 10 ways to choose it. There are 13,650 ways.
3 chocolate and 2 mint are 15C3 * 10C2=20,475 ANSWER C
2 chocolate and 3 mint are 15C2*10C3=105*120=12,600
1 chocolate and 4 mints are 15C1*10C4=15*210=3150
0 chocolate and 5 mints are 15C0*10C5=10C5=252 ways
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At lest four mint candies are 3150+252=3402 ANSWER D
For chocolate, any, the answer is 3003+13,650+20,475+12,600+3150=52878. ANSWER B
A check on this OR an easier way to do answer B is to find the number of samples that contain only mints, which is 252. All the rest must contain chocolate.
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