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How many different ways are there to arrange a row of 4 men and 2 women so that no two women sit next to one another?

Option: 1

220


Option: 2

360


Option: 3

420


Option: 4

470


Answers (1)

best_answer

Given that,
No two women would be seated next to each other if they sit between men.
So, first, the men can be arranged in 4 ! ways.
There are 5 spots between the men.
The number of ways to arrange the 2 women in those 5 spots is given by,
            \begin{aligned} & { }^5 P_2=\frac{5 !}{(5-2) !} \\ & { }^5 P_2=\frac{5 \times 4 \times 3 \times 2}{3 \times 2} \\ & { }^5 P_2=20 \end{aligned}

So, the total number of ways is,

            4 ! \times 20=480

Therefore, the number of ways the seating arrangement is done in 480 ways.

Posted by

Irshad Anwar

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