In how many ways can 5 boys and 4 girls be seated on a bench so that the girls and the boys occupy alternate seats?​

Answer:

2880 ways

Step-by-step explanation:

There can be only one arrangement in which boys and girls can sit.

G-B-G-B-G-B-G-B-G

but position of individual boy and girls can be changed.

So, there are 5 girls and 5 slots for them that means they can be arranged in 5! ways,

similarly boys have 4 slots, so they can be arranged in 4! ways.

now, one more thing to consider is that out of 5! arrangements of girls, with each arrangement boys can be arranged in 4! different positions.

so to get the total number of boys and girls arrangements together we would need to multiply the arrangements of both boys and girls.

so the desired answer would be: 5!*4! = 120*24 = 2880 ways.

There are 2880 ways for 5 boys and 4 girls to be seated on a bench so that the girls and the boys occupy alternate seats.

The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to a variety of possible arrangements or orders. The arrangement's order is important when using permutations. A permutation is a way to arrange each component in the proper order. The combination is a choice of components from a group.

Given There are 5 girls and 4 boys needed to be seated on the bench so that boys and girls occupy alternate seats.

There can only be one seating arrangement for boys and girls.

G-B-G-B-G-B-G-B-G

However, the location of each boy and girl can be adjusted individually.

Girls can be ordered in 5 ways since there are 5 slots available for them, and boys can be placed in 4 ways because there are 4 slots available for them. There is also the fact that boys can be put in 4! distinct positions for each of the 5! configurations of girls.

Therefore, we would need to multiply both the boys' and girls' arrangements in order to determine the total number of boys' and girls' arrangements.

Therefore, 5!*4! = 120*24  or 2880 ways would be the desired response.

Learn more about permutations and combinations here:

https://brainly.com/question/28065038

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