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How many ways can 5 boys and 5 girls sit in a row so that no two boys are together?
There are equal numbers of boys and girls, so in order to keep the boys allseparated, there aren't enough girls for any of them to sit together either.The genders must alternate all the way, end to end. So one gender mustoccupy all even-numbered chairs, and the other gender must occupy allodd-numbered chairs.-- Number of ways the girls can occupy their 5 chairs = (5 x 4 x 3 x 2) = 120 ways.For each different way the girls are arranged . . .-- Number of ways the boys can occupy their 5 chairs = (5 x 4 x 3 x 2) = 120 ways.-- Total number of ways all ten of them can be arranged = 120 x 120 = 14,400 ways.-- AND ... each gender can take either the odd or the even seats, and the whole14,400 can be done either way. If the seats are numbered, then the total numberof ways to assign ten names to the ten numbered seats is 28,800.=================If there were no restriction on who could sit together, then the total numberof ways to arrange ten people would be10! = (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2) = 3,628,800 ways.
Two girls and four boys are to seated in a row in such a way that the girls do not sit together in how many different ways can it be done?
There are seven different layouts, if none of the people have identities. If each girl and boy must be identified, then there are 336 different layouts. Each of these can be doubled if the end that you start counting from is also defined.
How many ways can 8 people sit in 8 chairs?
555
How many ways can 4 people sit in 4 chairs?
128
How many different ways can 4 people be seated on a row of seats?
4 people seated on a row may have 4! = 4x3x2x1 = 24 different ways to sit.
