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# 10 t-shirts are available to choose. 5 of them are printed,

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10 t-shirts are available to choose. 5 of them are printed, [#permalink]  20 Jun 2004, 08:00
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10 t-shirts are available to choose. 5 of them are printed, and 5 of them are plain t-shirts. If 3 t-shirts are to be selected at random from the 10, what is the probability that at least one of them is a printed t-shirt.

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If the answer is 5/24, i will explain.
Manager
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P(all non-printed) = 5C3/10C3=5*4*3/10*9*8=1/12
P(atleast one printed)=1-1/12=11/12
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Senior Manager
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Pardon me GUEST ...

I can let know the answer only if you explain. Sorry about that.

Goal Stanford...

I understand the first step - Desired/Total combinations.

But

P(atleast one printed)=1-1/12=11/12 - Can you explain me this step?.

Thanks bro.
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Re: Combintions [#permalink]  20 Jun 2004, 23:17
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carsen wrote:
10 t-shirts are available to choose. 5 of them are printed, and 5 of them are plain t-shirts. If 3 t-shirts are to be selected at random from the 10, what is the probability that at least one of them is a printed t-shirt.

1. Probability of at least 1 being a printed = 1 - P(none of them is printed).

2. P(all 3 are plain) = 5/10*4/9*3/8 = 1/12!

3. The answer is 1 - 1/12 = 11/12.
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Re: 10 t-shirts are available to choose. 5 of them are printed, [#permalink]  14 Jul 2014, 19:41
do you mean how many methods or anything other?

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Re: 10 t-shirts are available to choose. 5 of them are printed, [#permalink]  14 Jul 2014, 20:58
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Expert's post
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carsen wrote:
10 t-shirts are available to choose. 5 of them are printed, and 5 of them are plain t-shirts. If 3 t-shirts are to be selected at random from the 10, what is the probability that at least one of them is a printed t-shirt.

You have 10 t-shirts. You need to choose 3 of them. You can do this in 10C3 = 10*9*8/3*2*1 = 120 ways.

You have 5 plain t-shirts. You can choose 3 out of them in 5C3 = 5*4/2 = 10 ways.

So you have total 120 ways of picking 3 t-shirts out of 10. In 10 of those ways, you pick all plain t-shirts. So what happens in the rest of the 110 ways? In those, you must be picking up at least one printed t-shirt.

So probability of picking at least one printed t-shirt = 110/120 = 11/12
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