Question

There are 5 girls and 6 boys. Find the number of arrangement if they are to be arranged in 2 rows,(1st row: 5 seats, 2nd row: 6 seats). The boys and girls must stand alternately.

Answer 1

@oldrin.bataku

Answer 2

You can youe the concept of Matrices

Answer 3

Doy you know how ?

Answer 4

no

Answer 5

But, wait you can solve it using combination

Answer 6

Umm maybe the use of permutation and combination?

Answer 7

yes

Answer 8

Is it 5C2 x 6C3 x (1st row):6.5.5.4.4 x (2nd row):3.3.2.2.1.1=17280000

Answer 9

Stand alternately?

Answer 10

boy girl boy girl

Answer 11

There are 5 girls and 6 boys. Find the number of arrangement if they are to be arranged in 2 rows,(1st row: 5 seats, 2nd row: 6 seats). The boys and girls must stand alternately.

There are \(5!\) ways to order the girls and you have \(2\) ways to seat them. For a particular seating of the girls, you end up with \(6!\) ways to order the boys in the remaining seats. I found \(5!\times6!\times2=172800\)

Answer 12

oops! there is actually only 1 way to seat them:
B G B G B G B G B G B
6 * 5 * 5 * 4 * 4 * 3 * 3 * 2 * 2 * 1 * 1

so forget the 2, only \(5!\times6!=86400\)

Answer 13

What about this, 1st row- B G B G B
6. 5. 5.4.4
2nd row- we can either start with a boy or a girl,
B G B G B G
3.3.2.2.1.1 so we multiply by 2 =172800

Answer 14

@nick96 you can't start with either boy or girl though

Answer 15

If you start with girls, observe:

G B G B G B G B G B B

Answer 16

But IF the question states that boy and girl stand alternately in a row ,then 172800 is correct right?