By how many ways 4 girls and 5 boys be arranged in a line so that : (i) all girls always together (ii) all girls never together
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Answer:
Step-by-step explanation:
No. Of girls = 4
No. Of boys =5
(i) For all girls to be together
Consider girls as one unit.
In that one unit the girls can be arranged in 4! Ways (since there are 4 girls)
Now there are 5 boys and 1 unit. Therefore they can be arranged in 6! Ways.
Therefore
Answer=
6! x 4! = 720 x 24 = 17280 ways
(ii) For all girls never together
Suppose the boys are already placed in alternate positions. The number of spaces for the girls to take place is 6
_B_B_B_B_B_
The boys can be arranged within themselves in 5! Ways.
The girls can be arranged in (6P4) ways.
Therefore answer is
(6P4) x 5! = 6!/(6-4)! x 120 = 43200 ways
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