Question

5 countries president and prime minister went for the summit. If all 5 prime minister shakes hand to a president at random, in how many ways they can shake hand if none of the same country PM shakes hand to that country president.

• A. 9
• B. 44
• C. 120
• D. 24

Answer 1

The correct option is B

44

Since none of the same country PM shakes hand to that country president none of the same country PM shakes hand to that country president

So, number of de arrangements
$D_n=n!{\sum }_n^{k=0}\frac{(-1{)}^k}{k!}$
=$5!(1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}-\frac{1}{5!})$
=44