SOLUTION: a restaurant offers 10 entrees. if a party of 6 arrives for dinner, whats the probability that at 2 people will choose the same entree..

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Question 408719: a restaurant offers 10 entrees. if a party of 6 arrives for dinner, whats the probability that at 2 people will choose the same entree..
Found 2 solutions by richard1234, sudhanshu_kmr:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Due to the Pigeonhole principle, there must be at least two people that order the same entrée (assuming each person orders one entrée). Therefore the probability is 1.

Answer by sudhanshu_kmr(1152) About Me  (Show Source):
You can put this solution on YOUR website!
No. of ways that a person choose the entree = 10

no. of ways that 6 person choose the entrees = 10*10*10*10*10*10= 10^6
no. of ways that all 6 person choose different entree = 10P6 =10*9*8*7*6*5

probability that all 6 person have different choice P(A)= 10P6/10^6
= 151200/10^6
= 1512/10^4

now, probability that at 2 people will same entree P(A') = 1- P(A)
= 1- ( 1512/10^4)
= 8488/10000