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# In a certain mathematical activity, we start with seven cards, each wi

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Re: In a certain mathematical activity, we start with seven cards, each wi [#permalink]
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Bunuel wrote:
In a certain mathematical activity, we start with seven cards, each with a different prime number written on it. These seven cards are randomly put into three boxes in the following way: one box must get four cards, one must get two, and one gets only one. Then, for each box, we find the product of all the cards in the box, and that’s the “number” of the box. Then, we put those three numbers in order, from lowest to highest, and that is our set. How many different sets can be created from this process?

(A) 35
(B) 105
(C) 210
(D) 420
(E) 630

Kudos for a correct solution.

Answer should be (B) 105

7! / 4! 2! 1!
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Re: In a certain mathematical activity, we start with seven cards, each wi [#permalink]
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Bunuel wrote:
In a certain mathematical activity, we start with seven cards, each with a different prime number written on it. These seven cards are randomly put into three boxes in the following way: one box must get four cards, one must get two, and one gets only one. Then, for each box, we find the product of all the cards in the box, and that’s the “number” of the box. Then, we put those three numbers in order, from lowest to highest, and that is our set. How many different sets can be created from this process?

(A) 35
(B) 105
(C) 210
(D) 420
(E) 630

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

Part of the logic of the problem involves recognizing that every unique combination of prime numbers produces a unique product. There is no way that two different groupings cards will produce the same set of numbers.

First of all, the cards to go into the cup holding 4 cards.

7C4 = 35.

Once we have placed 4 card in the first cup, we have three cards left, which means we have three choices of a single card to put into the third cup. Three choices. Once we place that, the remaining two cards must go into the second cup: no choice there.

N = 35*3 = 105

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Re: In a certain mathematical activity, we start with seven cards, each wi [#permalink]
7C4 *3C2 = 35 *3 = 105
correct answer option B
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Re: In a certain mathematical activity, we start with seven cards, each wi [#permalink]
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Re: In a certain mathematical activity, we start with seven cards, each wi [#permalink]
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