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Hi,

Im struggling how to intepret the following questions:

In how many ways can 3 boys and 3 girls sit in a row?

In how many ways can 3 boys and 3 girls sit in a row if the boys and the girls are eah to sit together?

in how many ways if just the boys to sit together?

Thanks for any help
Original post by helloimfred
Hi,

Im struggling how to intepret the following questions:

In how many ways can 3 boys and 3 girls sit in a row?

In how many ways can 3 boys and 3 girls sit in a row if the boys and the girls are eah to sit together?

in how many ways if just the boys to sit together?

Thanks for any help


For one, you have 6 objects. How many ways are the to arrange 6 objects?

For two, in how many ways can you arrange the seating so that all the boys are together, and all the girls are together?? I.e. you cannot have BGBBGG because the second person (G) is separated from the rest of the girls. Likewise with the first boy.

For three, it's a similar concept as the part before, except now we don't care about the girls sitting together, so we are allowing to have something like GBBBGG. In how many ways can we have all the boys sitting together?
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helloimfred
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Original post by RDKGames
For one, you have 6 objects. How many ways are the to arrange 6 objects?

For two, in how many ways can you arrange the seating so that all the boys are together, and all the girls are together?? I.e. you cannot have BGBBGG because the second person (G) is separated from the rest of the girls. Likewise with the first boy.

For three, it's a similar concept as the part before, except now we don't care about the girls sitting together, so we are allowing to have something like GBBBGG. In how many ways can we have all the boys sitting together?

So for two, i take it that the boys and girls are all distinguished so in each general ordering you have 3!*3! ways of ordering the boys and girls, and there are 4 ways of ordering them in general so is 4*3!*3! right?
Original post by helloimfred
So for two, i take it that the boys and girls are all distinguished so in each general ordering you have 3!*3! ways of ordering the boys and girls, and there are 4 ways of ordering them in general so is 4*3!*3! right?


Well, I'm unsure if you've been told to assume they are unique people.

In the case that we have B={b1,b2,b3}B = \{ b_1, b_2, b_3 \} (set of boys consists of three different boys) and G={g1,g2,g3}G = \{ g_1, g_2,g_3\}, then you are on the right lines.

I agree with 3! * 3! but I'm not sure where you got 4 from?

Surely there are only two ways to have it; either it goes (3 boys, 3 girls) or (3 girls, 3 boys). Each of these has 3!*3! possibilities.
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helloimfred
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Original post by helloimfred
So for two, i take it that the boys and girls are all distinguished so in each general ordering you have 3!*3! ways of ordering the boys and girls, and there are 4 ways of ordering them in general so is 4*3!*3! right?

actually thats wrong isnt it, is that the answer for 3 and is the answer for 2 the same but 2*
Original post by helloimfred
the answer is two times 3!*3! because you can have the 3 boys first or the 3 girls first


Agreed.

For three, it says we want *just* the boys sitting together. So we cannot have GGGBBB or BBBGGG like in the last part.
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helloimfred
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Original post by RDKGames
Agreed.

For three, it says we want *just* the boys sitting together. So we cannot have GGGBBB or BBBGGG like in the last part.

Yeah you would be right there but i made a mistake it said 'only the boys must sit together' so i guess the girls can sit together if they want, thanks

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