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29 Jan 2018, 05:44
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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
A. 12
B. 18
C. 36
D. 72
E. 720
29 Jan 2018, 06:08
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Bookmarks
Bunuel
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
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)
29 Jan 2018, 07:00
Kudos
Bookmarks
Bunuel
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
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
Answer: Option C
