Misc 9 - Chapter 6 Class 11 Permutations and Combinations

Transcript

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