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# There are 10 items, you will pick three items out of these

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Joined: 06 Jan 2006
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There are 10 items, you will pick three items out of these [#permalink]  19 Feb 2006, 13:23
There are 10 items, you will pick three items out of these 10, what is the probability that the items you pick contain the most expensive 2 of the 10?

How would you solve this problem? I don't really know where to start.
My tentative solution is 2/10 + 1/10 + 8/10 The first 2/10 is the probability of picking one of the two most expensive item, then 1/10 indicates picking the other one of the two, then 8/10 indicates everything else is fair game.

I think I'm totally going about this the WRONG way. How would you solve it? Probability problems give me migranes! .......
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Joined: 21 Sep 2003
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Here is what I think:

Total combinations = 10C3

Possibilities : All combninations where the two most expensive items appear

E1, E2, X (X cab be any of the other 8 items)
= 1*1*8 = 8

Reqd Probability = 8/10C3 = 1/15
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Total possibilites = 10C3 = 120
Assuming we have picked out 2 of the most expensive items, then third item can only be any one of the remainig 8. So total possibilites = 8

P = 8/120 = 1/15
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