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Carly has 3 movies that she can watch during the weekend: 1

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Carly has 3 movies that she can watch during the weekend: 1  [#permalink]

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New post 28 Oct 2006, 09:24
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Carly has 3 movies that she can watch during the weekend: 1 Action, 1 Comedy, and 1 Drama. However she needs to watch the Drama 3 times. Assuming Carly has time for 5 movies and intends to watch all of them, in how many ways can she do so?

1) 6
2) 20
3) 24
4) 60
5) 120

OPEN DISCUSSION OF THIS QUESTION IS HERE: carly-has-three-movies-that-she-can-watch-during-the-weekend-an-actio-256147.html

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Re: Carly has 3 movies that she can watch during the weekend: 1  [#permalink]

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New post 28 Oct 2006, 09:28
i would go for e. 120. but permutation and combination are my weak poitn so don't know if i'm correct.

got 120 by 5!

now someone give us the right answer :)
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Re: Carly has 3 movies that she can watch during the weekend: 1  [#permalink]

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New post 28 Oct 2006, 09:37
2) 20

Think of it as the word DDDCA, the number of ways of rearranging this is 5!/3!, where 5 is the total number and 3 is the number of repeating characters.

or

Ways of selecting 3 out of 5, 5C3 = 5!/3!2! = 10, then 2 ways of arranging the other 2, 10*2 = 20
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Re: Carly has 3 movies that she can watch during the weekend: 1  [#permalink]

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New post 19 Dec 2007, 14:09
Since Carly has to watch the drama 3 seperate times, you can really consider it 3 different movies. 5!/3!=20.
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Re: Carly has 3 movies that she can watch during the weekend: 1  [#permalink]

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New post 25 Dec 2017, 11:50
uvs_mba wrote:

Carly has 3 movies that she can watch during the weekend: 1 Action, 1 Comedy, and 1 Drama. However she needs to watch the Drama 3 times. Assuming Carly has time for 5 movies and intends to watch all of them, in how many ways can she do so?

1) 6
2) 20
3) 24
4) 60
5) 120


Carly has three movies that she can watch during the weekend: an action movie, a comedy, or a drama. However, she wants to watch the same drama movie three times, an action movie once and a comedy movie also once. In how many different ways can she arrange these five screenings?

A. 6
B. 20
C. 24
D. 60
E. 120


The number of different ways Carly can watch Drama, Drama, Drama, Action, Comedy (DDDAC) is basically the number of arrangements of 5 letters DDDAC out of which 3 D's are identical, so it's \(\frac{5!}{3!}=20\).


Answer: B

OPEN DISCUSSION OF THIS QUESTION IS HERE: carly-has-three-movies-that-she-can-watch-during-the-weekend-an-actio-256147.html

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Re: Carly has 3 movies that she can watch during the weekend: 1 &nbs [#permalink] 25 Dec 2017, 11:50
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