Question

permutations: 24) how many ways can 3 boys and 3 girls sit in a row if a) no restrictions on where they sit in a row b) all boys sit together and all girls sit together c) only boys must sit together, the girls choosing their seats?

Answer 1

for b) i got 20! divided by 3!3!.. so 20 ways is that correct?

Answer 2

how many ways can 3 boys and 3 girls sit in a row if a) no restrictions on where they sit in a row

There's 6 kids, so just order all six: 6!

b) all boys sit together and all girls sit together

Imagine them them in groups of 3... then there's two groups of 3 kids. Eg if a, b, c are the boys and d, e, f, the girls, then they're in groups (a, b, c) and the girls are in a group (d, e, f)

There's 2 groups to arrange, and 3 kids which can be arranged within their group:

2!*3!*3!

Answer 3

wouldnt there be more than 6 ways for a

Answer 4

because

Answer 5

6! does not equal 6... 6! = 6*5*4*3*2*1

Answer 6

oh sorry i thought i saw a 6

Answer 7

what about c?

Answer 8

is it 3! x 2

Answer 9

c) only boys must sit together, the girls choosing their seats?

The boys are again together like (a, b, c). The girls can be put anywhere, eg d, (a,b,c) e, f - imagine it like there's one group of boys, and then three groups of girls (with only one girl in each group)

So there's four groups total (4!), then the three boys in a group (3!) then each of the girls (1! for each)

4!*3!*1!*1!*1!