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:

So the probability of at least one duplication is:

You can do the arithmetic.

John

My calculator said it, I believe it, that settles it