Respuesta :
Answer:
The correct option is 4.
Step-by-step explanation:
It is given that 10 men and 12 women will be seated in a row of 22 chairs.
Total possible ways to arrange n terms is n!.
Similarly,
Total possible ways to place 22 people on 22 chairs = 22!
[tex]\text{Total outcomes}=22![/tex]
It is given that all men will be seated side by side in 10 consecutive positions.
Total possible ways to place 10 people on 10 chairs = 10!
Let 10 men = 1 unit because all men will be seated side by side in 10 consecutive positions. 12 women = 12 units because women can any where.
Total number of units = 12 + 1 = 13.
Total possible ways to place 13 units = 13!
Total possible ways to place 10 men and 12 women, when all men will be seated side by side in 10 consecutive positions is
[tex]\text{Favorable outcomes}=10!\cdot 13![/tex]
The probability that all men will be seated side by side in 10 consecutive positions
[tex]P=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}=\frac{10!\cdot 13!}{22!}[/tex]
Therefore the correct option is 4.
