How numerous ways deserve to 8 civilization be sit in a row? if there are 4 men and also 4 women and also no 2 men or women may sit beside each other.

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I walk it together follows,As 4 men and also 4 women have to sit beside each various other so we think about each the them together a solitary unit.Now we have actually we 4 people(1 guys group, 1 women group, 2 males or women) they have the right to be sit in 4! ways.Now every of the team of men and women can swap places within us so we need to multiply the answer through 4!*4! This provides the full 4!*4!*4! =13824 .Please aid me out through the answer. Room the actions clear and is the answer and also the an approach right?

Thanks

If over there is a guy on the first seat, there needs to be a woman on the second, a male on the 3rd so forth. Alternatively, we can start through a woman, then put a man, climate a woman and so forth. In any kind of case, if us decide which sex to put on the very first seat, the genders because that the others seats are compelled upon us. So over there are just two means in i m sorry we have the right to divide the eight to adjust seats into "man-seats" and "woman-seats" there is no violating the rule that no two men and also no 2 women may sit alongside each other.

Once you have actually chosen where to chair the men and also where the females you deserve to permute the two groups arbitrarily, providing $4!$ possibilities each. So in full the variety of possible constellations is$$2\cdot 4!\cdot 4!=1152.$$

Look , we have actually 8 human being , 4 of lock are males , 4 the them are women , we need to put every man and also woman together , it means we will have actually 4 groups of men and women sitting together. , to gain Group1 we have 4 possibilities of guys , and 4 possibilities of women , climate to get Group2 us left through 3 men and 3 ladies , then in the very same manner we got : 4*4*3*3*2*2*1*1 =576 (4!*4!) , so lastly we left just with combine of the teams in the range , together I got there 4! # of combine this groups .So i guess this is the price : 4!*4!*4!

Is it that no 2 men and also no two women need to be sit together. Yep? Then carry out this..Permutation of guys in 4 places be 4!. This leaves us through 5 gaps(3 in between and 2 on one of two people side) in i m sorry we gained to arrange 4 women.. P(5,4) i.e. 5! ways.Finally 5!*4! is the answer!.

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In how numerous ways can $14$ people be sit in a heat if there space $8$ men and they should sit beside one another?