Q26 of 31 Page 7

If there are 7 boys and 5 girls in a class, then in how many ways they can be seated in a row such that:

(i) No two girls sit together? (iii) All the girls never sit together?

(i) No two girls sit together



In the figure assume that girls can sit in × positions.


As there 8 positions where girls can sit and there are 5 girls.


So, 5 girls can sit in 8P5 ways.


And 7 boys can sit in 7! Ways.


So total ways = 8P5× 7!





= 8× 7× 6× 5× 4× 3× 2× 1×7×6×5×4


= 33868800 ways


(ii) All the girls never sit together.


Total number of ways in which no 2 girls sit together = Total arrangements – Number of arrangements in which girls sir together


Total arrangements = 12C12 = 12! Ways


Total ways = 12! - 8P5× 7!


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