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Permutation with Flash Cards

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by beeparoo » Thu May 29, 2008 12:44 pm
A first grade teacher uses ten flash cards, each numbered from 1 to10, to teach her students to order numbers correctly. She has students choose four flash cards randomly, then arrange the cards in ascending order. One day, she removes the cards '2' and '4' from the deck. On that day, how many different correct arrangements of four randomly selected cards are possible?

A. 70
B. 210
C. 336
D. 840
E. 1680

OA after a few responses... Promise!
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Re: Permutation with Flash Cards

by mim3 » Thu May 29, 2008 1:47 pm
beeparoo wrote:A first grade teacher uses ten flash cards, each numbered from 1 to10, to teach her students to order numbers correctly. She has students choose four flash cards randomly, then arrange the cards in ascending order. One day, she removes the cards '2' and '4' from the deck. On that day, how many different correct arrangements of four randomly selected cards are possible?

A. 70
B. 210
C. 336
D. 840
E. 1680

OA after a few responses... Promise!
I'm going to go with A.
8p4= 1680
#of ways to arrange four cards: 24

1680/24= 70

Not confident in that answer at all.
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by getneonow » Thu May 29, 2008 10:51 pm
Overall there should be 10 cards but 2 are removed now.

So 8 cards left out.

Now if we select any 4 cards from these 8, we can always arrange them in ascending order since all the cards are distinct.

Thus ans will be 8C4 = 70

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by beeparoo » Fri May 30, 2008 11:17 am
Ans is A. 70

Good job, guys

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by Mclaughlin » Sat May 31, 2008 12:21 pm
getneonow wrote:Overall there should be 10 cards but 2 are removed now.

So 8 cards left out.

Now if we select any 4 cards from these 8, we can always arrange them in ascending order since all the cards are distinct.

Thus ans will be 8C4 = 70

Neo
Stupid question but in your asnwer you wrote 8C4. what does that mean? what does C represent in this equation?
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by Stuart@KaplanGMAT » Sat May 31, 2008 8:49 pm
Mclaughlin wrote:
getneonow wrote:Overall there should be 10 cards but 2 are removed now.

So 8 cards left out.

Now if we select any 4 cards from these 8, we can always arrange them in ascending order since all the cards are distinct.

Thus ans will be 8C4 = 70

Neo
Stupid question but in your asnwer you wrote 8C4. what does that mean? what does C represent in this equation?
"C" represents "choose" or "combination".

nCk = n!/k!(n-k)!

when n = total # of objects and k = the # chosen

In this question, we have 8 total cards and we're choosing 4 of them. If we want to know the number of subgroups of 4 that we can choose out of 8 total, we have:

n=8, k=4

8C4 = 8!/4!(8-4)! = 8!/4!4! = 8*7*6*5*4*3*2/4*3*2*4*3*2 = 8*7*6*5/4*3*2 = 7*6*5/3 = 7*2*5 = 70
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