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5 co workers, part of a car pool drive to work. There are two seats in the front including the driver's seat and three at the back. If John or Kevin who are a part of this pool have to drive the car, then in how many ways can the 5 be seated in the car?

Is the answer to the permutation question 4!*2?

While we are at it, can you please tell me the answer for this question?

In how many ways can 4 black balls that are identical and 4 white balls that are identical be arranged such that black and white balls alternate?

Ashok - Your answer to the car pool question is right.

For the question that you had asked "In how many ways can 4 black balls that are identical and 4 white balls that are identical be arranged such that black and white balls alternate?"

The answer is 2 ways.

The arrangement can either start with a white ball and have white balls in the first, third, fifth and seventh place. And black balls at the even numbered positions.

Or have the white balls in the first, third, fifth and seventh place. And white balls at the even numbered positions.

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why not 2 * 4! * 4! ?

the white balls can re arrange in 4! ways and so can the black balls

The balls are identical is what the question states.

4 identical objects can rearrange in 4 places in exactly 1 way and not in 4! ways.

Hence, the answer is 2 ways. And not 2 * 4! * 4!