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If 3 girls and 3 boys must sit in a row of six chairs but [#permalink]

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15 Nov 2006, 20:45

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If 3 girls and 3 boys must sit in a row of six chairs but boys are not allowed to sit beside one another, how many different seating arrangements can be made?

Imagine there are 6 seats __ __ __ __ __ __ . Let the boys seat in the first, third, and fifth seat. There are 3*2*1 arrangement for boys. For the second, fourth and sixth seats, apply the same logic, we have 6 arrangement for girls. So in total, there are 6*6 = 36 arrangement.

let 3 girls be seated in !3 ways..and in between them ,there r 4 places in which 3 boys have to be seated and that can be done by selecting 3 out of 4 places(4c3 ways) and filling the 3 boys in !3 ways...
hence !3 * 4c3 * !3 ways = 144

i dont know where i missed it.
what's the oa???

quote="Pokhran II"]If 3 girls and 3 boys must sit in a row of six chairs but boys are not allowed to sit beside one another, how many different seating arrangements can be made?

let 3 girls be seated in !3 ways..and in between them ,there r 4 places in which 3 boys have to be seated and that can be done by selecting 3 out of 4 places(4c3 ways) and filling the 3 boys in !3 ways... hence !3 * 4c3 * !3 ways = 144

i dont know where i missed it. what's the oa???

quote="Pokhran II"]If 3 girls and 3 boys must sit in a row of six chairs but boys are not allowed to sit beside one another, how many different seating arrangements can be made?

(A) 12 (B) 36 (C) 72 (D) 180 (E) 720

[/quote]

There are only 6 chairs so once 3 girls take 3 chairs the remaning 3 boys are left with 3 chairs only (though there are 4 spots available)

Re: If 3 girls and 3 boys must sit in a row of six chairs but [#permalink]

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25 Sep 2017, 20:05

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