Misc 9 - It is required to seat 5 men and 4 women in a row

Misc 9 - Chapter 7 Class 11 Permutations and Combinations - Part 2
Misc 9 - Chapter 7 Class 11 Permutations and Combinations - Part 3

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Misc 9 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? There are total 9 people Since women occupy even places Places 2, 4, 6, 8 will be occupied by women And Rest will be occupied by men The seating arrangement will be follows Now, we have to arrange 5 women and 4 men Arrangements of 4 women 4 women can sit in 4 positions Total number of ways = 4P4 = 4!/(4 − 4)! = 4!/0! = 4!/1 = 4 × 3 × 2 × 1 = 24 ways Arrangements of 5 men 5 men can sit in 5 positions Total number of ways = 5P5 = 5!/(5 − 5)! = 5!/0! = 5!/1 = 5 × 4 × 3 × 2 × 1 = 120 Thus, Total number of arrangements = 24 × 120 = 2880

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.