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# A gardener is going to plant 2 red rosebushes and 2 white

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Joined: 08 Nov 2008
Posts: 38
A gardener is going to plant 2 red rosebushes and 2 white  [#permalink]

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11 Dec 2008, 14:38
A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them in a row, what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes?

A. 1/12
B. 1/6
C. 1/5
D. 1/3
E. 1/2

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SVP
Joined: 30 Apr 2008
Posts: 1841
Location: Oklahoma City
Schools: Hard Knocks
Re: rose  [#permalink]

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11 Dec 2008, 14:51
B. 1/6

We're not treating this as 4 separate rose bushes, but 1 group of white (made up of 2 bushes) and 1 group of red (made up of 2 bushes).

If we had 4 separate rose bushes, that'd be 4! combinations, but we must divide out 2 because of the 2 red bushes (if you kept the white in place and swapped out the red, you'd still have the same color arrangement) and then divide again by 2 for the same situation with keeping the red in place and swapping the white.

so 24 / 2 = 12...12/2 = 6. Now, only 1 of these color combinations has W R R W, for 1/6.
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SVP
Joined: 29 Aug 2007
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Re: rose  [#permalink]

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11 Dec 2008, 15:02
gorden wrote:
A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them in a row, what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes?

A. 1/12
B. 1/6
C. 1/5
D. 1/3
E. 1/2

TOTAL = 4!
2R IN THE MIDDLE = 2X2 = 4 AS UNDER

W1 R1 R2 W2
W1 R2 R1 W2
W2 R1 R2 W1
W2 R2 R1 W1

= 4/4!
= 1/6

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Re: rose &nbs [#permalink] 11 Dec 2008, 15:02
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# A gardener is going to plant 2 red rosebushes and 2 white

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