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# A diificult math, pls explain

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Joined: 05 Jun 2011
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A diificult math, pls explain [#permalink]

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24 Jul 2011, 04:00
00:00

Difficulty:

35% (medium)

Question Stats:

78% (01:31) correct 22% (00:20) wrong based on 9 sessions

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In how many arrangements can a teacher seat 3 girls and 3 boys in a row of 6 seats if the boys are to have the first, third and fifith seats

a)6
b)9
c)12
d)36
e)720

pls explain~
[Reveal] Spoiler: OA
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Re: A diificult math, pls explain [#permalink]

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24 Jul 2011, 04:32
tracyyahoo wrote:
In how many arrangements can a teacher seat 3 girls and 3 boys in a row of 6 seats if the boys are to have the first, third and fifith seats

a)6
b)9
c)12
d)36
e)720

pls explain~

use the slot method _ _ _ _ _ _
boy in first place = 3 ways
in the 3rd place = 2 ways
5th place = 1 way
total 3*2*1 = 6 ways

similarly for girls
total 6*6 = 36 ways
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Re: A diificult math, pls explain [#permalink]

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24 Jul 2011, 16:31
Note that this is the same as asking "how many ways can 3 boys and 3 girls be arranged such that the boys sit in the first three chairs?"

The ways to arrange 3 boys: $$3! = 6$$
The ways to arrange 3 girls: $$3! = 6$$

Combined, $$3! * 3! = 6 * 6 = 36$$
Re: A diificult math, pls explain   [#permalink] 24 Jul 2011, 16:31
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