# propability on picking tickets in a box with six people

I am with a group of five of my friends. A box contains 8 airline tickets each of first class, business class, and economy class. The box is passed around the six of us, with each person taking 4 pieces. Assume that each person chooses at random without replacement from the available tickets. I am the last person to whom the box is passed.

i) Find the chance that I pick 4 economy tickets.

Total tickets in the box= 3*8each(FBE)=24tickets

Number of friends including me=n=6

P(A Picking 4 economy tickets)= 8C4/24C4=(70/10626)

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Do you really have any choice as to which tickets to get? – DJohnM Apr 19 '13 at 2:16

The position of the trial does not matter . It does not affect the outcome of any of the others. Each trial has the same chance to have the desired outcome. So the question is what is the chance for the desired outcome to happen.

P(4 economy tickets)=8/24*7/23*6/22*5/21=8C4/24C4

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Thanks Xenofon Sevastakis – juniorgraduation2013 Apr 22 '13 at 6:23

Possible sets of four tickets is just 24 choose 4; the possible sets of four economy tickets is 8 choose 4. Since all sets are equally likely, the ratio of these is what you want.

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Thanks Sharkos for Your Clear Explanation Understood – juniorgraduation2013 Apr 19 '13 at 20:16

Since you're the last one to pick tickets, and given the setup of the problem there are only four tickets left in the box when it gets to you, you're looking for the probability that the last four tickets are Economy class.

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Thanks Steve Beresh for you clear explanations! – juniorgraduation2013 Apr 19 '13 at 20:15