How countless ways deserve to 8 people be sit in a row? if there are 4 men and also 4 women and also no 2 males or women might sit next to each other.

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I go it together follows,As 4 men and 4 women have to sit next to each other so we consider each of them as a single unit.Now we have actually we 4 people(1 males group, 1 females group, 2 guys or women) they deserve to be seated in 4! ways.Now every of the group of men and also women deserve to swap places within themselves so we must multiply the answer with 4!*4! This renders the total 4!*4!*4! =13824 .Please aid me out v the answer. Space the measures clear and is the answer and also the method right?

Thanks

If there is a man on the very first seat, there has to be a mrs on the second, a male on the 3rd so forth. Alternatively, we can start v a woman, then put a man, climate a woman and also so forth. In any kind of case, if we decide which gender to placed on the first seat, the genders for the others seats are compelled upon us. So there are only two methods in i beg your pardon we have the right to divide the eight set seats right into "man-seats" and "woman-seats" there is no violating the dominion that no two men and no two women might sit beside each other.

Once you have actually chosen wherein to chair the men and also where the females you deserve to permute the two groups arbitrarily, giving $4!$ possibilities each. Therefore in total the number of possible constellations is$$2cdot 4!cdot 4!=1152.$$

Look , we have actually 8 human being , 4 of castle are men , 4 of them room women , we have to put every man and woman with each other , it means we will have 4 groups of men and women sitting together.

Is it the no 2 men and also no 2 women must be seated together. Yep? Then perform this..Permutation of guys in 4 areas be 4!. This pipeline us v 5 gaps(3 in between and 2 on one of two people side) in i beg your pardon we acquired to species 4 women.. P(5,4) i.e. 5! ways.Finally 5!*4! is the answer!.

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