A family consisting of one mother, one father, two daughters and a son is taking a road trip in a sedan. The sedan has two front seats and three back seats. If one of the parents must drive and the two daughters refuse to sit next to each other, how many possible seating arrangements are there?

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120

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Official Explanation

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As most of the combination problems this one can be solved in more than 1 way:

Sisters sit separately:

One of them is on the front seat (2 ways). Others (including second sister) can be arranged in: 2 (driver's seat) * 3! (arrangements of three on the back seat) = 12 ways. Total for this case: 2 * 12 = 24.

Both by the window on the back seat (2 ways). Others can be arranged in: 2 (driver's seat) * 2 (front seat) * 1 (one left to sit between the sisters on the back seat) = 4 ways. Total for this case = 8.…

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What this question tests

What it tests

Your handling of square and higher roots, including simplifying radicals.

Common trap

Forgetting the ± when taking a square root to solve an equation, or assuming √(a²) = a.