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# Combinations problem

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Intern
Joined: 27 Dec 2004
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Combinations problem [#permalink]  07 Feb 2005, 20:15
Team,

Would you mind helping me with this problem?

Question

A mother bird has 6 babies. Every times she returns to the nest, she feeds half the babies. If it takes her 5 minutes to feed each baby, how long will it take it to feed all the possible combinations of three babies?

Ans: 5 hrs[/u]
GMAT Club Legend
Joined: 07 Jul 2004
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Okay, here's how I'll solve it. The baby birds are all going to be the same, so order of feeding them doesn't matter.

So the possible number of combinations = 6!/3!3! = 20 combinations

Each combination comprise of 3 birdlings and each will take 5 minutes to feed. Therefore for 1 combination, it will take 3*5=15minutes

For 20 combinations: 20*15 = 300 minutes = 5 hours.
VP
Joined: 25 Nov 2004
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6C3=(6X5X4X3!)/[(3!)(6-3)!]=(6X5X4X3!)/(3X2X3!)=20
total time=20X(3X5 minuets)=600 minuets
SVP
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Re: Combinations problem [#permalink]  07 Feb 2005, 23:07
Johnnyman wrote:
Team,

Would you mind helping me with this problem?

Question

A mother bird has 6 babies. Every times she returns to the nest, she feeds half the babies. If it takes her 5 minutes to feed each baby, how long will it take it to feed all the possible combinations of three babies?

Ans: 5 hrs[/u]

C(6,3)=20
Each combination have three babies, and it takes her 5 minutes to feed each baby
So total time = 20*3*5=300 minutes = 5 hrs

During this time each baby has had 10 worms.

However, it is not really likely this happens. Since everytime when she returns the possibility of her picking one of the 20 combinations is 1/20. The possibility of her picking all the 20 combinations in 20 rounds of feeding is quite slim, I think. Any thoughts on this?
Manager
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6C3 * 5 * 3 = 600 min = 5 hrs.
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