Question

A team of 6 players consisting of 4 boys and 2 girls are chosen from a group of 8 boys and 5 girls. Find the number of ways the team members can be arranged in a row if the girls sit next to each other.

which answer is more accurate? 240 or 168000

Answer 1

is this one question or two?

Answer 2

we pick 4 out of 6 boys in \(\binom{8}{4}=70\) ways and similarly choose 2 out of 5 girls in \(\binom{5}{2}=10\) ways. so the number of possible teams is \(70\times 10=700\) and that is before we start seating them

Answer 3

1 question only. Yeah 100, but how many arrangement we can have with 4boys and 2 girls? is it 2P2x 4P4 x 5 = 240 ? then we need to find the arrangement of 4 boys out of the 8 and 2 girls from the 4 with 240 x 700 = 168000?

Answer 4

once we have the 700 possible teams, we can figure out how many ways we can arrange the 6 players in such a way that the girls sit next to each other
first we can think of the two girls as one, and the 6 seats as 5 and compute \(5!\) but then we have to multiply by 2 because the girls can trade places, so i believe the answer to the second part is \(2\times 5!\)

Answer 5

now if we multiply we get \(700\times 5!\times 2=168,000\)

Answer 6

what is this doing back open?