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by knight247 » Mon Sep 19, 2011 2:34 am
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) x 48 x 47
(B)(13^4) x 24 x 47
(C)48C6
(D)13^4
(E)(13^4) x 48C6

Slight change made. OA is B
Last edited by knight247 on Mon Sep 19, 2011 7:13 am, edited 2 times in total.
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by cans » Mon Sep 19, 2011 3:41 am
total 52 cards.
select 1 card each from each deck: 13*13*13*13.
now remaining 2 cards can be any. left cards=48. thus 48*47
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by shankar.ashwin » Mon Sep 19, 2011 3:58 am
I think ordering should not matter for the last 2 cards, so shouldnt it be 48c2? I dont see an option.


cans wrote:total 52 cards.
select 1 card each from each deck: 13*13*13*13.
now remaining 2 cards can be any. left cards=48. thus 48*47
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by shankar.ashwin » Mon Sep 19, 2011 4:01 am
Found this https://www.beatthegmat.com/choose-6-car ... 45411.html
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by knight247 » Mon Sep 19, 2011 5:07 am
My take
The first card does not matter. We can pick any one of the 52 cards. 52 Ways=13*4
The second card has to be from the remaining 3 decks decks i.e. 39C1= 39 Ways=13*3
The third card has to be from the remaing 2 decks i.e. 26C1=13*2 ways
The fourth card has to be from the last remaining deck i.e. 13C1=13 Ways
The last two can be picked from anyone of the remaining 48 cards i.e. 48C2=48*47/2=24*47 Ways

Multiplying all the ways together
13*4*13*3*13*2*24*47=13^4*24^2*47
Got it...However for the first four cards we have considered ordered sequences hence we need to divide by 4! as order is not important.

13^4*24^2*47/4!=13^4*24*47 Hence B Finally..hehe
Last edited by knight247 on Mon Sep 19, 2011 7:12 am, edited 1 time in total.
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by amit2k9 » Mon Sep 19, 2011 6:50 am
the first 4 cards are = 13^4
remaining cards = 52-4=48

last two cards will be = 48*47

thus 13^4 * 48*47.

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by knight247 » Mon Sep 19, 2011 7:44 am
@amit

U've made it into an ordered sequence brother. The answer is B
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by GMATGuruNY » Mon Sep 19, 2011 8:25 am
Ignore this problem.
It is far too complex for the GMAT.
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by knight247 » Fri Oct 07, 2011 11:41 pm
@Mitch
Can u plz confirm if my reasoning is correct! Thanks
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by GMATGuruNY » Sat Oct 08, 2011 6:38 am
knight247 wrote:@Mitch
Can u plz confirm if my reasoning is correct! Thanks
As I noted in my post above, I would ignore this problem.
It is far too complex for the GMAT.
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