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Romashka-Z-Leto [24]
3 years ago
6

10 men and 12 women will be seated in a row of 22 chairs. What is the probability that all men will be seated side by side in 10

consecutive positions? 1/C(22, 10) 10!/C(22, 10) 10!/22! 10! middot 12!/22! 10! middot 13!/22!
Mathematics
1 answer:
-BARSIC- [3]3 years ago
5 0

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!

\text{Total outcomes}=22!

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

\text{Favorable outcomes}=10!\cdot 13!

The probability that all men will be seated side by side in 10 consecutive positions

P=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}=\frac{10!\cdot 13!}{22!}

Therefore the correct option is 4.

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=================================

How to get this answer:

We're told that AD = BC, so that is one pair of sides that are congruent. This forms the first "S" in "SAS"

The "A" refers to the congruent angles, which happen to be angle DAB and angle CBA, both are 90 degrees

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