sana.noor wrote:In how many ways can 5 boys and 3 girls be seated on 8 chairs so that no two girls are together?
A 5760
B 14400
C 480
D 56
E 40320
OA is B
Number of ways to arrange the 5 boys = 5! = 120.
Each girl must occupy a position TO THE LEFT or TO THE RIGHT of a boy:
__B__B__B__B__B__
Number of options for the first girl = 6. (Any of the 6 slots above.)
Number of options for the second girl = 5. (Any of the 5 remaining slots.)
Number of options for the third girl = 4. (Any of the 4 remaining slots.)
To combine all of these options, we multiply:
120 * 6 * 5 * 4 = 14,400.
The correct answer is
B.
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