NIMCET 2010 — Reasoning PYQ

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Question

NIMCET 2010 — Reasoning PYQ

NIMCET | Reasoning | 2010

Steel Express runs between Tata Nagar and Howrah and has five stoppages in between. Find the number of different kinds of one-way second class ticket that Indian Railway will have to print to service all types of passenger who might travel by Steel Express?

Choose the correct answer:

Explanation

Solution

1. Identify the total number of stations:

Starting Station: Tata Nagar (1)
Intermediate Stoppages: 5
Ending Station: Howrah (1)
Total stations ( $n$ ) = $1 + 5 + 1 = 7$

2. Understanding the ticket requirement:

A "one-way" ticket is defined by a specific Starting Station and a specific Destination Station.

There are $7$ possible stations to start from.
For any chosen starting station, there are $6$ other stations that could be the destination.

3. Calculation using Permutations ( $^{n}P_{r}$ ):

Since the order of stations matters for a ticket (Station A to Station B is one type of ticket), we use the permutation formula where we select 2 stations out of 7:

\text{Total tickets} = ^{7}P_{2}

\text{Total tickets} = \frac{7!}{(7 - 2)!}

\text{Total tickets} = \frac{7 \times 6 \times 5!}{5!}

\text{Total tickets} = 7 \times 6 = 42

Correct Option: (b) 42