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# A homework assignment calls for students to write 5 sentence

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A homework assignment calls for students to write 5 sentence [#permalink]  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]  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)

=\frac{(10*9)}{2} *\frac{(8*7)}{2} * \frac{(6*5)}{2} * \frac{(4*3)}{2} *\frac{(2*1)}{2}

=\frac{10!}{32}
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Re: A homework assignment calls for students to write 5 sentence   [#permalink] 10 Oct 2017, 04:31
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