Final answer:
To solve the seating arrangement problem, calculate the permutations by first treating each pair of girls as a single entity. Then multiply the arrangements of the boys and pairs by the arrangements within each pair. The result is 20160, but this answer does not match any of the provided options.
Step-by-step explanation:
The problem is to find the number of ways in which 5 boys and 4 girls can be seated in a straight line if the girls are to be seated in two separate pairs. In this scenario, we treat each pair of girls as a single entity, and thus temporarily reduce the problem of arranging 4 girls into the simpler problem of arranging 2 pairs. Additionally, since the arrangement of girls within each pair matters, we must also account for the permutations within each pair of girls.
First, we arrange the 5 boys and the 2 pairs (which is effectively treating each pair as one unit). This gives us 7! (seven factorial) different arrangements. 7! equals 7 x 6 x 5 x 4 x 3 x 2 x 1 which is 5040 arrangements.
Next, we need to account for the arrangements of the girls within each pair. Since each pair has 2 girls, there are 2! arrangements for each pair, which equals 2 x 1, or 2 arrangements per pair. Since there are 2 pairs, we raise 2! to the power of 2, giving us 2!^2, which equals 4 arrangements.
Finally, we multiply the number of arrangements of the pairs with the number of arrangements within each pair to find the total number of arrangements: 7! x 2!^2 = 5040 x 4 = 20160 possible arrangements.