Answer:
Explanation:
To solve this problem, we'll consider the arrangements of the two groups: the two brothers who want to stand together and the three boys who want to stand together. Since the four girls don't mind where they stand, we can treat them as a single entity. Thus, we have three groups: (2 brothers), (3 boys), and (4 girls).
Now, let's calculate the number of ways we can arrange these three groups within the queue:
1. For the group of 2 brothers who want to stand together:
Since there are two brothers, they can arrange themselves in 2! (2 factorial) ways.
2. For the group of 3 boys who want to stand together:
Similarly, the three boys can arrange themselves in 3! (3 factorial) ways.
3. For the group of 4 girls (treated as a single entity):
Since the girls don't mind where they stand, they can be arranged among themselves in 4! (4 factorial) ways.
Now, we need to find the total number of arrangements by considering all the combinations of the three groups:
Total number of arrangements = (Number of arrangements of brothers) * (Number of arrangements of boys) * (Number of arrangements of girls)
Total number of arrangements = 2! * 3! * 4!
Total number of arrangements = 2 * 6 * 24
Total number of arrangements = 288
So, there are 288 ways to form the queue with the given conditions