SOLUTION: 6 friends go out for dinner and order from a menu of 8 different sandwiches. What is the probability that at least 2 of the group order the same sandwich?
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Question 573882: 6 friends go out for dinner and order from a menu of 8 different sandwiches. What is the probability that at least 2 of the group order the same sandwich?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
There are exactly two possibilities: Either at least 2 have the same sandwich or everyone has a different sandwich. Hence the probability that at least 2 have the same sandwich is equal to 1 minus the probability that they all have different sandwiches. So what, you say? Calculating the probability that they all have different sandwiches is a much simpler calculation, that's so what.
The probability that the first guy will order a different sandwich than everyone else is certainty. There are eight different sandwiches and he can choose any of the eight without duplicating anyone.
The second guy only has 7 sandwiches to choose because one of the possible 8 was already used by the first guy, hence his probability of not duplicating is 
Repeating the pattern through all six guys, the probability of no duplication is:
!8^6})
So the probability of at least one duplication is:
!8^6})
You can do the arithmetic.
John
My calculator said it, I believe it, that settles it
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