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How many different ways are there to draw 7 cards from a standard deck

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Bunuel
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How many different ways are there to draw 7 cards from a standard deck [#permalink] New post   25 May 2021, 00:48
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A
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56% (01:31) correct 44% (01:58) wrong based on 55 sessions
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How many different ways are there to draw 7 cards from a standard deck of cards and obtain 3 jacks and 4 queens if order does not matter?

A. 3
B. 4
C. 12
D. 35
E. 5040
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Re: How many different ways are there to draw 7 cards from a standard deck [#permalink] New post   25 May 2021, 01:00
Every card in a deck of cards comes in 4 suits. In this question we are asked how many different ways are there to draw 4 Queens and 3 Jacks. As all the queens will be drawn, focus only on the Jacks. How many ways can 3 Jacks be drawn from 4 Jacks. 4!/3!1! = 4

Answer B
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Re: How many different ways are there to draw 7 cards from a standard deck [#permalink] New post   02 Jun 2021, 13:47
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Order does not matter, so its a combination question -

need to select 3 jacks out of available 4 AND 4 queens out of available 4

=>4C3 * 4C4
=4*1 = 4
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Re: How many different ways are there to draw 7 cards from a standard deck [#permalink] New post   02 Jun 2021, 20:46
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All 4 queens can be drawn in 1 way (Taking all)

3 Jacks out of 4 can be drawn in \(^4{C_3} = 4\) ways.

Total: 1 * 4 = 4

Answer B
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Re: How many different ways are there to draw 7 cards from a standard deck [#permalink]
02 Jun 2021, 20:46
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