How many ways deserve to 8 world be sit in a row? if there space 4 men and also 4 women and no 2 men or women might sit next to each other.

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I did it together follows,As 4 men and also 4 women must sit beside each various other so we consider each the them together a single unit.Now we have actually we 4 people(1 guys group, 1 women group, 2 men or women) they have the right to be seated in 4! ways.Now each of the team of men and women can swap locations within themselves so we need to multiply the answer v 4!*4! This makes the full 4!*4!*4! =13824 .Please aid me out v the answer. Room the measures clear and is the answer and the an approach right?

Thanks

If there is a male on the first seat, there needs to be a woman on the second, a man on the third so forth. Alternatively, we can start v a woman, then put a man, climate a woman and so forth. In any case, if us decide which gender to placed on the very first seat, the genders for the others seat are forced upon us. So there are only two means in i m sorry we can divide the eight to adjust seats right into "man-seats" and "woman-seats" without violating the preeminence that no 2 men and no 2 women may sit beside each other.

Once you have chosen where to seat the men and also where the ladies you have the right to permute the two groups arbitrarily, giving $4!$ possibilities each. Therefore in complete the number of possible constellations is$$2\cdot 4!\cdot 4!=1152.$$

Look , we have 8 civilization , 4 of lock are males , 4 that them room women , we have to put every man and also woman together , it means we will have actually 4 teams of men and also women sit together. , to gain Group1 we have actually 4 possibilities of guys , and also 4 possibilities of ladies , then to obtain Group2 we left with 3 men and 3 women , climate in the exact same manner we acquired : 4*4*3*3*2*2*1*1 =576 (4!*4!) , so ultimately we left only with combine of the teams in the variety , as I got there 4! # of combinations this groups .So i guess this is the prize : 4!*4!*4!

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

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In how plenty of ways deserve to $14$ civilization be sit in a heat if there are $8$ men and they have to sit next to one another?