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A first grade teacher uses ten flash cards, each numbered fr [#permalink]

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11 Sep 2005, 17:10

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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?

i think i'm missing something here, if arrangement/order is a part of this problem why is it considered a combination problem as opposed to a permutation one?

Re: PR '05 A teacher uses ten flash cards, numbered 1 through [#permalink]

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20 Mar 2014, 17:17

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Yes, I have the same doubt. I really don´t understand the solution. Book solution: Make four spots for the cards chosen, and then fill in the number of options for each spot:

8 x 7 x 6 x 5

Then divide by the number of ways to arrange theses four cards: 4 x 3 x 2 x 1
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Encourage cooperation! If this post was very useful, kudos are welcome "It is our attitude at the beginning of a difficult task which, more than anything else, will affect It's successful outcome" William James

i think i'm missing something here, if arrangement/order is a part of this problem why is it considered a combination problem as opposed to a permutation one?

It's not advisable to tag the questions using its wording. Just because the question uses the word 'arrangement', it doesn't make this an arrangement problem. It is a combination problem and here is why: When you pick the cards, there is only one way in which you can arrange them - the ascending order which will be unique for any 4 cards you pick. Say, I picked up 3, 5, 6, 10. The only way I can arrange them is this: 3, 5, 6, 10. I cannot arrange them as 3, 6, 10, 5 or 6, 5, 3, 10 or any other arrangement that you can have with 4 unique cards. The number of arrangements here is not 4!. Instead it is only 1 since they must be put in ascending order.

So all you have to do is find out the number of ways in which you can pick 4 cards out of 8 unique cards. This will be done in 8C4 = 70 ways.

The book uses the basic counting principle. Put 4 cards in 4 places in 8*7*6*5 ways and since you can arrange them in only one way, divide by the number of arrangements i.e. 4!

When will it be an arrangement problem? "She has students choose 4 cards randomly, then arrange the cards in ANY order." Now each selection will have 4! distinct arrangements.
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Re: A first grade teacher uses ten flash cards, each numbered fr [#permalink]

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02 May 2015, 07:28

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A first grade teacher uses ten flash cards, each numbered fr [#permalink]

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26 May 2016, 08:20

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A first grade teacher uses ten flash cards, each numbered fr [#permalink]

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28 Jul 2016, 23:05

The question appears to be a tough one but I have opted for a simpler approach Let me know if I am wrong when we choose 4 cards then in order to have them arrangement in an ascending order(or any order) there will only be one way.(think over it or do it yourself practically). Hence if total number of cards are 10 and we have to choose 4 out of it then there will only be ONE arrangement and no of combinations given by 10C4 but here 2 cards have been removed so 10-2=8 cards remain now according to the previous approach

Re: A first grade teacher uses ten flash cards, each numbered fr [#permalink]

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31 Aug 2017, 03:18

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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