Question

In a cricket match against Pakistan, Azhar wants to bat before Jadeja and Jadeja wants to bat before Ganguli. Number of possible batting orders with the above restrictions if the remaining eight team members are prepared to bat at any given place is

• A. $\frac{11!}{3!}$
• B. ${}^{11}{P}_3$
• C. $\frac{11!}{3}$
• D. none

Answer 1

The correct option is A $\frac{11!}{3!}$

This is $0$ question of restricted permutation.

We have $11$ places

Let us put ( Azhar, Jadeja, Ganguli) as a sequence.

We have different cases, Azhar can't bat $10$ down.

If he has to bat $9$ down then Jadeja is $10$ down and Ganguli at $11.$

Remaining $8$ places cab be done in $8!$ ways.

Similarly doing this for all cases and adding we get,

$=\frac{11!}{3!}$

Hence the answer is $\frac{11!}{3!}.$