5 boys and 4 girls are to be seated in a row such that all boys are together?

Case I : asking for number of arrangements

No. of arrangements
= (No. of arrangements for 4 girls and a group of boys) × (No. of internal arrangements of the group of boys)
= P(5,5) × P(5,5)
= 5! × 5!
= 14400


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Case II : asking for probability

No. of arragements without restriction
= P(9,9)
= 9!

P(5 boys and 4 girls are to be seated in a row such that all boys are together)
= 5!5!/9!
= 5/126