NIMCET 2025 Paper

Section: Mathematics

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?

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

Validate

Solution:

There are 5 captains in total.
Treat the India-Australia pair as one block.
Then total arrangements:
- Treat (IA) as 1 unit

⟶ 4

units total

⟶ 4

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

⟶ 2

! arrangements
Favorable

=4!× 2=24 × 2=48

Total possible arrangements

=5!=120

Probability:

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

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