There are 10 persons named `P_1, P_2, P_3 ..., P_10`. Out of 10 persons, 5 persons are to be arranged in a line such that is each arrangement `P_1` must occur whereas `P_4` and `P_5` do not occur. Find the number of such possible arrangements.

Explanation

We need to arrange 5 persons in a line out of 10 persons, such that in each arrangement `P_1` must occur whereas `P_4` and `P_5` do not occur.

First we choose 5 persons out of 10 persons, such that in each arrangement `P_1` must occur whereas `P_4` and `P_5` do not occur.

Number of such selections `=>^7 C_4`

Now, in each selection 5 persons can be arranged among themselves in `5 !` ways.

`therefore` required number of arrangements ` 7_(C_4) times 5 !`
`=>
frac(7 times 6 times 5)(3 times 2 times 1) times 5 times 4 times 3 times 2 times 1=>4200`

Thus, number of such possible arrangements is 4200 .