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At a certain pet show, exactly 6 dogs are entered in the bea

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At a certain pet show, exactly 6 dogs are entered in the bea [#permalink] New post 16 Jun 2018, 10:18
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At a certain pet show, exactly 6 dogs are entered in the beagle division and exactly 6 are entered in the dalmatian division. If the top 3 dogs in each division receive first-, second-, and third-place ribbons respectively, with no other dogs receiving a prize, how many different ways can ribbons be awarded to winners in the two divisions together?


A. 28,800

B. 14,400

C. 720

D. 400

E. 36
[Reveal] Spoiler: OA

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Re: At a certain pet show, exactly 6 dogs are entered in the bea [#permalink] New post 21 Jun 2018, 23:24
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here is the answer
in the first group 3 dogs can receive the award in 6*5*4 = 120 ways
in the second group 120 ways
total ways = 120*120= 14400
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Re: At a certain pet show, exactly 6 dogs are entered in the bea [#permalink] New post 27 Oct 2020, 01:41
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In the first group, winner group containing 3 dogs can be formed in 6C3 ways - prizes can now be distributed in group 1 in 6C3*3! ways = 120.
In the second group, winner group containing 3 dogs can be formed in 6C3 ways - prizes can now be distributed in group 2 in 6C3*3! ways = 120.

Total no of ways in which prizes can be distributed in group 1 & group 2 together = 120 * 120 = 14400
Re: At a certain pet show, exactly 6 dogs are entered in the bea   [#permalink] 27 Oct 2020, 01:41
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At a certain pet show, exactly 6 dogs are entered in the bea

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