I am very confused about permutation and combination, here are two questions I a

Question

I am very confused about permutation and combination, here are two questions I am trying to deal with.

1. in how many ways a team of 3 can be formed from 9 men and 11 women if (a) they have to be 1 men and 2 women? (b) regardless of sex?

2. in how many ways can 6 people can seated on 7 chairs around a round table if (a) only their positions relative to each other count (that is, the arrangements obtained from each other by rotation of all people are considered to be the same); (b) only who sits next to whom counts, but not on which side( rotaions and reflections do not change the arrangement?)

Hope someone can help me out. For best answer, please with deatiled steps and explaination. I really appreciate.

Explanation / Answer

1. in how many ways a team of 3 can be formed from 9 men and 11 women if

(a) they have to be 1 men and 2 women?

Solution:- 9c1*11c2 = 9*55 = 495

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(b) regardless of sex?

sol :- 20c3 = 1140

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2) in how many ways can 6 people can seated on 7 chairs around a round table if

(a) only their positions relative to each other count (that is, the arrangements obtained from each other by rotation of all people are considered to be the same);

sol:- (6-1)!*2 = 240

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(b) only who sits next to whom counts, but not on which side( rotaions and reflections do not change the arrangement?

sol:- (6-1)!* = 120

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Done please rate sir !!!

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