Question

In how many ways can 10 friends be seated in a straight line such that two friends a and b never sit together

Answer 1

Answer:

Between 2 Friends a will sit at the middle and between 2 Friends b will sit at the middle

I Hope it's help u

Answer 2

The correct answer is 3265920.

Given: Number of friends = 10.

a and b can never sit together.

To Find: In how many ways can 10 friends be seated in a straight line such that two friends a and b never sit together.

Solution:

Number of ways in which 10 friends can be seated without restriction = 10!.

Number of ways that a and b can never sit together = Total ways - number of ways in which a and b always sit together

For number of ways in which a and b always sit together tie a and b together and assume them as 1 quantity. So now we are left with 9 friends.

And to arrange 9 friends = 9!

Number of ways that a and b can never sit together = 10! - 9!

= 9! (10 - 1)

= 9! x 9

= 3265920.

Hence, 3265920 ways are there to arrange 10 friends be seated in a straight line such that two friends a and b never sit together.

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