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Combination incorrect mgmat

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Senior | Next Rank: 100 Posts
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by Jinglander » Fri Sep 24, 2010 5:10 pm
Ok here is a problem from mgmat that I don't agree with the answer. Please advise

Amy and Adam are making boxes of truffles for as wedding favors. They have an unlimited supply of 5 different types of truffles. If each box holds 2 truffles of different types how many different boxes can they make.

The book says it's 5!/3!2! but this seems wrong since there is a unlimited supply. Instead I would think u have 5 choices for the first and 4 for the second hense 20
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by Rahul@gurome » Fri Sep 24, 2010 7:26 pm
Though there is an unlimited supply of truffles, their types is limited which is 5 in number.
Let the types be a, b, c, d, and e.

Each box can have 2 truffles of different types.
So what we need to do is to find out the number of ways in which we can select 2 types out of the 5 types which is 5C2 = 5!/(3!2!) = 10.

You can see that the different boxes possible are ab, ac, ad, ae, bc, bd, be, cd, ce, de and they are 10 in number.
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