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NIMCET 2025 Paper

Section: Mathematics

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Question : 28 of 120

Marks: +1, -0

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

$\; \frac{1}{5}$
$\; \frac{1}{4}$
$\; \frac{1}{2}$
$\; \frac{2}{5}$

Solution:

There are 5 captains in total.

Treat the India-Australia pair as one block.

Then total arrangements:

- Treat (IA) as 1 unit

\rightarrow 4

units total

\rightarrow 4

! arrangements

- Inside the block, (IA) or (AI)

\rightarrow 2

! arrangements

Favorable

=4! \times 2 = 24 \times 2 = 48

Total possible arrangements

=5! = 120

Probability:

\; \frac{48}{120} = \; \frac{2}{5}

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