Seating in a row with a block condition: Four boys and two girls are to be seated in a straight line such that the two girls are always together (treated as an adjacent pair). In how many distinct linear arrangements can they be seated?

Introduction / Context:This is a classic permutations-with-a-block problem. When two specified people must sit together in a line, we can temporarily treat them as a single unit while counting arrangements, then multiply by the internal permutations of that block.

Given Data / Assumptions:

• Individuals: 4 distinct boys and 2 distinct girls.
• Constraint: the two girls must be adjacent.
• Order matters, and all persons are distinct.

Concept / Approach:

• Treat the two girls as one “block” to honor adjacency.
• Count permutations of the resulting units in a row.
• Multiply by internal arrangements of the two girls within their block.

Step-by-Step Solution:

Verification / Alternative check:Direct adjacency counting using positions for the pair also leads to the same product 5! * 2! = 240, confirming the result.

Why Other Options Are Wrong:

• 120 counts the five units but misses the internal 2! for the girls.
• 720 is 6! ignoring the adjacency constraint.
• 148 is not a standard permutation count from this setup.

Common Pitfalls:

• Forgetting the internal permutations of the two girls.
• Accidentally counting 6! without enforcing adjacency.

Final Answer:240