In how many ways can 3 boys and 2 girls be arranged on a bench if all boys wish to sit together?Group of answer choices24364860

To solve this problem, we need to consider the group of boys as a single entity. So, we have 3 entities to arrange: the group of boys and the 2 girls.

Step 1: Arrange the entities We can arrange these 3 entities in 3! (3 factorial) ways, which is 321 = 6 ways.

Step 2: Arrange the boys within their group The 3 boys can be arranged among themselves in 3! (3 factorial) ways, which is 321 = 6 ways.

Step 3: Multiply the results The total number of arrangements is the product of the number of ways to arrange the entities and the number of ways to arrange the boys within their group. So, 6*6 = 36 ways.

So, the 3 boys and 2 girls can be arranged on a bench in 36 ways if all boys wish to sit together.