First slide

Permutations

Question

The number of ways in which seven persons can be arranged at a round table, if two particular persons may not sit together is

Easy

A

480
B

120
C

80
D

None of these

Solution

Remaining 5 can be seated in 4! ways.
Now, on cross marked five places 2 person can sit in $^{5} P_{2}$ ,
ways.
So, number of a:nangements
$\begin{array}{l} = 4! \times \frac{5!}{3!} \\ = 24 \times 20 = 480 ways \end{array}$

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