If 6 boys and 3 girls are to be seated in a row for a photograph, then the probability that the end seats are occupied by the girls and no two girls are side by side is

Step-by-step solution

Total number of arrangements of 6 boys and 3 girls in a row is 9! . For the end seats to be occupied by girls, we can select and arrange 2 girls out of 3 in ³P₂ = 6 ways. The remaining 1 girl and 6 boys are to be seated in the remaining 7 middle seats. To ensure no two girls are side by side, the remaining 1 girl cannot sit in the seats adjacent to the ends (i.e., the 2nd and 8th seats). Thus, the remaining girl can sit in any of the 5 available middle seats (3rd, 4th, 5th, 6th, or 7th). The 6 boys can then be arra