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A homework assignment calls for students to write 5 sentence

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Bunuel
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A homework assignment calls for students to write 5 sentence [#permalink] New post   09 Oct 2017, 23:11
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A homework assignment calls for students to write 5 sentences using a total of 10 vocabulary words. If each sentence must use two words and no words can be used more than once, then how many different ways can a student select the words?

(A) 10!/5!

(B) 10!/32

(C) 5! x 5!

(D) 2! x 5!

(E) 10!

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Re: A homework assignment calls for students to write 5 sentence [#permalink] New post   10 Oct 2017, 04:31
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Bunuel wrote:
A homework assignment calls for students to write 5 sentences using a total of 10 vocabulary words. If each sentence must use two words and no words can be used more than once, then how many different ways can a student select the words?

(A) 10!/5!

(B) 10!/32

(C) 5! x 5!

(D) 2! x 5!

(E) 10!

Kudos for correct solution.


Now we have to write 5 sentence from 10 vocabulary words and each sentence must have two words

Therefore we can use the combination i.e 10C2 * 8C2 * 6C2 * 4C2 * 2C2 (5 sentences we have write and no words can be repeated)

=(10∗9)2∗(8∗7)2∗(6∗5)2∗(4∗3)2∗(2∗1)2

=10!32
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Re: A homework assignment calls for students to write 5 sentence [#permalink] New post   04 Jun 2020, 20:42
CHANGE KEY TO B
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Re: A homework assignment calls for students to write 5 sentence [#permalink] New post   17 Jun 2020, 12:44
Can you explain why you divide by 2?
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Re: A homework assignment calls for students to write 5 sentence [#permalink] New post   17 Jun 2020, 13:24
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n!k!(n−k)!

10∗9∗8∗7∗6∗5∗4∗3∗2∗12∗1(8∗7∗6∗5∗4∗3∗2∗1)=

10∗92
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Re: A homework assignment calls for students to write 5 sentence [#permalink] New post   17 Jun 2020, 13:31
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momspaghetti wrote:
Can you explain why you divide by 2?


As Carcass explained, 10C2 = (10)(9)/2!

Here's a video that covers how to calculate combinations (like 10C2) in your head:
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Re: A homework assignment calls for students to write 5 sentence [#permalink] New post   15 Dec 2020, 04:53
Very complex!
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Re: A homework assignment calls for students to write 5 sentence [#permalink] New post   19 Jun 2024, 03:44
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep 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 homework assignment calls for students to write 5 sentence [#permalink]
19 Jun 2024, 03:44
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