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Question
3 boys and 3 girls are to sit in a row. How many ways can this be done if there is a girl at each end
Solution
The two ends can be occupied by 3 girls in 3P2 ways.
After this the remaining 4 persons can sit at remaining 4 places in 4P4 ways.
Hence, the total number of seating arrangements
= 3P2 × 4P4
= `(3!)/(1!) xx 4!`
= 3 × 2 × 1 × 4 × 3 × 2 × 1
= 144.
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