Question

find the number of ways to arrange 5 people P1, P2.... P5 in a row such that P1 is neither first person nor last person in a row ​

Answer 1

Given:

P1 to P5 arranged in a row such that P1 neither gets the first and the last position.

To Find:

Number of ways it can be done.

Solution:

In  one row there are 5 positions.

Since,1st and 2nd position can't be taken by one person .

So, the person can occupy the reamining three places in the middle.

⇒3P1.

Now we have 4 persons left and the ways they can occupy the seats=4!

Therefore the total number of ways =3P1$\times$4!.