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Tamil Nadu Board of Secondary EducationHSC Science Class 11

8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another? - Mathematics

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Question

8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?

Sum
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Solution

Since no two men be together they have to be placed between

8 women and before and after the women.

w | w | w | w | w | w | w | w

There are 9 places so the 6 men can be arranged in the 9 places in 9P6 ways.

After this arrangement, the 8 women can be arranged in 8! ways.

∴ Total number of arrangements = (9P6) × 8!

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Chapter 4: Combinatorics and Mathematical Induction - Exercise 4.2 [Page 178]

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Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board
Chapter 4 Combinatorics and Mathematical Induction
Exercise 4.2 | Q 8. (iii) | Page 178

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