Permutations and CombinationsMCQMTP June 24 Series IQuestion 1676 of 251
All Questions

A garden having 6 tall trees in a row. In how many ways 5 children stand, one in a gap between the trees in order to pose for a photograph?

Options

A24
B120
C720
D30
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Correct Answer

✅ Option b — 120

All Options:

  • A24
  • B120
  • C720
  • D30

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Detailed Solution & Explanation

We are given 6 tall trees standing in a row in a garden. Let us denote the trees from left to right as T1,T2,T3,T4,T5,T6\displaystyle T_1, T_2, T_3, T_4, T_5, T_6.

The gaps *between* these adjacent trees are:
1. Gap 1: between T1\displaystyle T_1 and T2\displaystyle T_2
2. Gap 2: between T2\displaystyle T_2 and T3\displaystyle T_3
3. Gap 3: between T3\displaystyle T_3 and T4\displaystyle T_4
4. Gap 4: between T4\displaystyle T_4 and T5\displaystyle T_5
5. Gap 5: between T5\displaystyle T_5 and T6\displaystyle T_6

Thus, there are exactly 5 gaps between the 6 trees.
We have 5 distinct children, and we must place exactly one child in each gap.
This is equivalent to finding the number of ways to arrange the 5 distinct children into the 5 distinct gaps. The number of such linear arrangements is:
5!=5×4×3×2×1=120 ways5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \text{ ways}

Hence, **Option B** is the correct answer.

About This Chapter: Permutations and Combinations

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Factorials, Permutations, Combinations

This chapter deals with the fundamental principles of counting. It covers factorials, circular permutations, restricted permutations, combinations, and the differences between selecting items versus arranging them.

View Official ICAI Syllabus

Exam Strategy Tip

The most common mistake is confusing 'P' (Arrangement) with 'C' (Selection). If order matters (like opening a lock), use P. If order doesn't matter (like choosing a team), use C.

Related Comparison Tables

Permutations vs Combinations: The Quantitative Aptitude Guide

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