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Question
3 boys and 3 girls are to sit in a row. How many ways can this be done if all boys sit together
Solution
Three boys can sit together in 3P3 ways. Now considering 3 boys as 1 group, 3 girls and 1 group of boys, i.e., altogether 4 can sit in 4P4 ways.
Hence, the total number of seating arrangements in which all boys sit together
= 3P3 × 4P4
= 3!4!
= 3 × 2 × 1 × 4 × 3 × 2 × 1
= 144.
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