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.
- 36
- 84
- 100
- 120
The Correct Option is A
Solution and Explanation
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.
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