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# In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages

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Math Expert
Joined: 02 Sep 2009
Posts: 58313
In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages  [#permalink]

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29 Jan 2018, 05:44
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Difficulty:

15% (low)

Question Stats:

81% (01:09) correct 19% (00:46) wrong based on 77 sessions

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In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages if the cats must be in the second, fourth, and sixth cages?

A. 12
B. 18
C. 36
D. 72
E. 720

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In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages  [#permalink]

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29 Jan 2018, 06:08
Bunuel wrote:
In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages if the cats must be in the second, fourth, and sixth cages?

A. 12
B. 18
C. 36
D. 72
E. 720

The arrangement of the cats in the cages will be as follows
D C D C D C

The three cats can be arranged in 3! ways
Similarly, the 3 dogs can be arranged in 3! ways

Therefore, the total ways the pets can be lined up is $$3!*3! = 6*6$$ = 36(Option C)
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Re: In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages  [#permalink]

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29 Jan 2018, 07:00
Bunuel wrote:
In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages if the cats must be in the second, fourth, and sixth cages?

A. 12
B. 18
C. 36
D. 72
E. 720

The cages for the cats are fixed however the order of cats in those cages may vary in 3! ways

The cages for the Gods are fixed (remaining cages after cats are closed in respective cages) however the order of dogs in those cages may vary in 3! ways

Hence total favorable ways to arrange cats and dogs in cages = 3!*3! = 36

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Re: In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages  [#permalink]

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29 Jan 2018, 11:19
Total combinations = 3!*3!
6*6 = 36
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Re: In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages  [#permalink]

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30 Jan 2018, 11:19
Bunuel wrote:
In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages if the cats must be in the second, fourth, and sixth cages?

A. 12
B. 18
C. 36
D. 72
E. 720

Our arrangement must be as follows:

D - C - D - C - D - C

For the first cage, we have 3 possibilities because there are 3 available dogs for the first cage. For the second cage, we have 3 possibilities for the 3 available cats. For the third cage, we have 2 available dogs (because one dog was already placed in the first cage). Similarly, for the fourth cage, we have 2 available cats. Finally, for the fifth cage, we have the one remaining dog, and for the sixth cage, the one remaining cat. .

So, the number of ways to arrange the animals is 3 x 3 x 2 x 2 x 1 x 1 = 36.

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Re: In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages   [#permalink] 30 Jan 2018, 11:19
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