Permutations and CombinationsPYQ May 25Question 4326 of 183
All Questions

Seema, Bharati, Priyanka, Khusboo and Lalita are 5 speakers. The number of ways in which Seema will always speak before Bharati shall be -

Options

A24
B4! x 2!
C5!
D12
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Correct Answer

✅ Option a — 24

All Options:

  • A24
  • B4! x 2!
  • C5!
  • D12

Detailed Solution & Explanation

There are 5 speakers: Seema, Bharati, Priyanka, Khusboo, and Lalita. The total number of permutations for arranging 5 speakers is:
5!=1205! = 120

**Case 1: If \"before\" means \"immediately before\" (Textbook interpretation)**:
In this case, Seema must speak immediately before Bharati. We can treat (Seema, Bharati) as a single entity in that specific order. This leaves us with 4 entities to arrange: (Seema, Bharati), Priyanka, Khusboo, and Lalita.
The number of arrangements is:
4!=244! = 24
This matches Option a.

**Case 2: If \"before\" means \"any time before\" (Symmetric mathematical interpretation)**:
By symmetry, in exactly half of all the 120 permutations, Seema will speak before Bharati, and in the other half, Bharati will speak before Seema. This gives:
1202=60 ways\frac{120}{2} = 60 \text{ ways}
Since 60 is not in the options, the textbook author assumes Seema speaks immediately before Bharati. Therefore, we use the first interpretation.
Hence, **Option A** 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.

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