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PERMUTATIONS AND COMBINATIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPERMUTATIONS AND COMBINATIONS3 Marks
Question
It is required, to seat 5 men, and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?
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Answer

Here we have 5 men and 4 women. It is given that women occupy the even places.

1

2

3

4

5

6

7

8

9

M

W

M

W

M

W

M

W

M


Here we have four even places. So we can arrange four womens in 4! ways and 5 men in 5! ways in remaining five places.
$\therefore $ Required number of ways $ = 4! \times 5!$
$ = 24 \times 120 = 2880$

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