In how many ways 4boys and 5girls sit in a row if boys and girls must alternate?

Question

Explain how... thanks...

Answer 1

With the alternation requirement, row must start and end with girls and have boys between. 5! = 120 ways to arrange the girls, 4! = 24 ways to arrange the boys, so 120(24) = 2880.

Answer 2

boys = 4*3*2*1 = 24 (so the boys can sit in 24 different patterns)

girls = 5*4*3*2*1 = 120 (so the girls can sit in 120 different patterns)

multiply together to get the overall settings
120*24 = 2280

Answer 3

Philo got it.

Here's another way to think about it:

First position: 5 choices of girls
Second: 4 choices of boys
Third: 4 choices of girls
4th: 3 choices of boys
5th: 3 choices of girls
6th: 2 choices of boys
7th: 2 choices of girls
8th: 1 choice of boy
9th: 1 choice of girl

Multiply the number of choices and you get Philo's answer (5! * 4!) = 2880

The numbers of choices by positions
5*4*4*3*3*2*2*1*1 = 2880

Answer 4

Seat one, 6 options (start up with all and sundry) --Say we began with a woman, (3 boys 2 ladies left after determination) Seat 2, 3 options (must be opposite intercourse of selection a million) --We began with a woman, so this must be between the three boys left (2 boys 2 ladies left after determination) Seat 3, 2 options (must be opposite intercourse of selection 2) --final spot replaced right into a boy, this must be one in all the two ladies left (2 boys, a million lady left after determination) Seat 4, 2 options (must be opposite intercourse of selection 3) --final spot replaced right into a woman, this must be one in all the two boys left (a million boys, a million lady left after determination) Seat 5, a million options (must be opposite intercourse of selection 4) --final spot replaced right into a boy, this must be between the a million ladies left (a million boys, 0 lady left after determination) Seat six, a million options (must be opposite intercourse of selection 5) --in basic terms a million selection left, the suitable boy Multiply 6*3*2*2*a million*a million = seventy two

Answer 5

isnt it just 9^9?

because there are 9 people and 9 seats. So each person can sit on 1 of 9 seats.