Question

$25$ buses are running from $P$ and $Q$ stations. In how many ways can a person go from $P$ to $Q$ and return by a different bus.

• A. $600$
• B. $576$
• C. $625$
• D. None of these

Answer 1

The correct option is A $600$

$25$ Buses from $P$ to $Q$

A person goes from $P$ to $Q$

Chances that he returns in diffrent bus

He has to select diffrent bues are required

so nmber of ways

${}^{25}{P}_2[{}^n{P}_r=\frac{n!}{(n-r)!}]\Rightarrow \frac{25\times 24\times 23!}{23!}\Rightarrow 25\times 24$

$\Rightarrow 600$ Ways