Question

Five students are to be arranged on five chairs for a photograph. Three of these are girls and the rest are boys. Find out the total number of ways in which three girls are together.

• A. 36
• B. 84
• C. 100
• D. 120

Answer 1

The Correct Option is A

To solve this problem, we need to calculate the total number of ways to arrange five students on five chairs such that the three girls are together.

Consider the three girls as a single unit or "block." This block, combined with the two boys, constitutes three units to be arranged:

• The "girls block"
• Boy 1
• Boy 2

The number of ways to arrange these three units is the same as finding permutations of these three units:

Number of arrangements of 3 units = 3! = 6

Within the "girls block," the three girls can be arranged among themselves in:

3! = 6 ways.

Therefore, the total number of ways to arrange the students such that the three girls are together is:

Total arrangements = 3! × 3! = 6 × 6 = 36.

Thus, the correct answer is 36.