Question

There are 10 stations on a railway line. The number of different journey tickets that are required by the authorities is:

• A. 92
• B. 90
• C. 91
• D. None of these

Hint:

Think of each ticket as an ordered choice of a start and end station: use permutations directly, or combinations doubled for direction.

Answer 1

The Correct Option is B

Look at this as arranging 2 stations out of 10 in a strict order, since the start and end station of a ticket are different roles.

1. 92: this number does not come from any valid ordered-pair or pair-times-two count for 10 stations, so it is wrong.
2. 90: this is what we get from $10 \times 9 = 90$, counting ordered choices of a start and a distinct end station.
3. 91: close to 90 but off by one, it does not match the clean product $10 \times 9$.
4. None of these: ruled out once we confirm 90 is correct.

The correct count is 90, because there are 10 ways to pick the start station and, once that is fixed, 9 ways to pick a different end station, giving $10 \times 9 = 90$ ordered pairs, each pair being one ticket.

Let's summarize:

• 10 stations give $10 \times 9 = 90$ ordered station pairs.
• Each ordered pair is exactly one ticket, so 90 tickets are needed.

This confirms option B without needing to first pick unordered pairs and double them.