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# In how many ways can one choose 6 cards from a normal deck

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Manager
Joined: 23 Mar 2008
Posts: 216
In how many ways can one choose 6 cards from a normal deck [#permalink]

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17 Aug 2008, 01:49
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In how many ways can one choose 6 cards from a normal deck of cards so as to have all suits present?

a) (13^4)*48*47
b) (13^4)*27*47
c) 48C6
d) 13^4
e) (13^4)*48C6
Director
Joined: 27 May 2008
Posts: 540
Re: PS: cards [#permalink]

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17 Aug 2008, 05:55
puma wrote:
In how many ways can one choose 6 cards from a normal deck of cards so as to have all suits present?

a) (13^4)*48*47
b) (13^4)*27*47
c) 48C6
d) 13^4
e) (13^4)*48C6

first make sure we have atleast one card from each suit
so number of ways getting 4 cards, one of each suits = 13^4
now we are left with 48 cards we need to draw 2 more, with no restrictions, numebr of ways = 48C2 = 48*47/2 = 24*47

total number of ways = (13^4)*24*47 ... Not an option .....

could you check the question...
Intern
Joined: 21 Jul 2008
Posts: 5
Re: PS: cards [#permalink]

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17 Aug 2008, 10:46
I agree with durgesh79..

On second thoughts, is the answer (A) ?

4 cards from 4 suits = 13^4

Now the 5th card can be drawn in 48 ways and the 6th one in 47 ways

So the number of ways = 13^4 * 48 * 47
Re: PS: cards   [#permalink] 17 Aug 2008, 10:46
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# In how many ways can one choose 6 cards from a normal deck

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