NIMCET 2025 — Mathematics PYQ

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Question

NIMCET 2025 — Mathematics PYQ

NIMCET | Mathematics | 2025

The captains of five cricket teams, including India and Australia, are lined up randomly next to one other for a group photo. What is the probability that the captains of India and Australia will stand next to each other?

Choose the correct answer:

Explanation

1. Total possible arrangements:

The number of ways to arrange 5 captains in a row is:

\text{Total Outcomes} = 5! = 120

2. Favorable arrangements (India and Australia together):

Treat the captains of India and Australia as a single unit or "block".

Number of units to arrange: $(5 - 2) + 1 = 4$ units.
Ways to arrange these 4 units: $4!$
Ways India and Australia can swap places within their block: $2!$

\text{Favorable Outcomes} = 4! \times 2! = 24 \times 2 = 48

3. Probability calculation:

P(E) = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}}

P(E) = \frac{48}{120}

P(E) = \frac{2}{5}

Correct Answer: Option B