M men and n women are to be seated in a row so that no two women sit together. If m > n , m>n, then the number of ways in which they can be seated, is:
Answers
Answer with explanation:
→→It is given that, m men and n women are to be seated in a row so that no two women sit together.
Also, m> n
→→Suppose ,there are 3 men and 2 women ,whom we have to arrange in a row so that no two women sit together.
Men=a, b, c
Women = p, q
Total number of Arrangement
1. a p b q c, 2. b p a q c, 3. a q b p c, 4.b q a p c
5.c p b q a, 6. c q b p a, 7. c p a q b, 8.c q a p b
9. b p c q a 10. b q c p a 11. a p c q b 12. a q c p b
You have to put men at first place and women at second place , so there will be three places where men can be kept and there are 2 places where women can hold their seats ,as there are 3 different men which can be arranged in 3! ways,and 2 different Women which can be arranged in 2! ways,therefore total number of arrangement =3! ×2!=3×2×1×2=12 ways
→So,number of ways by which m Men and n Women are to be seated in a row,so that no two women sit together, If m > n,then men have to occupy odd places and Women has to Occupy even places.as there are m different men which can be arranged in m! ways,and n different Women which can be arranged in n! ways,
So ,total number of Arrangement = m! × n!
Answer:
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