4 boys and 4 girls are arranged to sit in a row. Find the number of arrangements that can be made if :
(a) there is no restriction,
>>>(4+4)!=40320<<<
(b) the boys must sit separately,
>>>4!*4!=576<<<
(c) 2 girls must sit at the ends.
>>>(8-1)!*2!=10080<<<
is it correct?
for b :-
(b) the boys must sit separately,
tie all 4 boys in one bag
remaining 4 girls separate.
so total 1 bag + 4 girls = 5 objects can be permuted in 5! ways
boys inside bag can be permuted in 4! ways
so total arrangements = 5!*4!
When boy must sit separately, girls must also sit separately, e.g.:
B G B G B G B G
Then 4!4! is correct for this case.
That's one arrangement. But you can also have a girl taking the first seat, i.e.
G B G B G B G B
So, you need to multiply your original answer by two.
You only need to fix two girls (of course you need to permute that two girls as well) at the end, the others, you can mix and match, let the rest permute themselves.
when two girls sit in the two ends they can do it in 2 ways so remaining 4 boys and 2 girls = 6 students can sit in 6! = 720 ways
total no of ways = 2x720 = 1440