Ih how many way can 5 boys and 4 girls be arranged in a row so that the boys and the girls stand alternatel (A) 28800 (B) 14400 (C) 2880 (D) 60480 Correct answer is C explain how?

Question

Answer

Arrangement of Boys and Girls in Alternating Pattern

To solve this problem, we need to consider that the boys and girls will stand alternately. This means that the first person in the row can be either a boy or a girl, and the second person in the row must be of the opposite gender. The pattern continues until all the boys and girls are arranged in the row.

Solution:

- First, we need to choose which gender will be in the first position. We can either choose a boy or a girl. Let's say we choose a boy.
- Then, we need to choose a girl for the second position. There are 4 girls to choose from.
- For the third position, we need to choose a boy. There are 5 boys to choose from.
- We continue in this pattern, alternating between boys and girls, until all 9 positions are filled.

Therefore, the total number of arrangements can be calculated as follows:

5 * 4 * 4 * 3 * 3 * 2 * 2 * 1 * 1 = 28,800

However, we need to divide by 2 since the first person in the row could have been a girl instead of a boy. This is because both options will give us the same alternating pattern. So, the final answer is:

28,800 / 2 = 14,400

Therefore, the correct answer is option (B) 14,400.

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