Permutations and CombinationsMCQPYQ Jun 19Question 1685 of 251
All Questions

If these are 40 guests in a party. If each guest takes a shake hand with all the remaining guests. Then the total number of hands shake is _________.

Options

A780
B840
C1,560
D1,600
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Correct Answer

✅ Option a — 780

All Options:

  • A780
  • B840
  • C1,560
  • D1,600

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Detailed Solution & Explanation

To find the total number of handshakes at a party of 40 guests where every guest shakes hands with every other guest exactly once, we use combinations.

A single handshake occurs between any unique pair of guests.
The total number of guests is N=40\displaystyle N = 40.
The number of ways to choose 2 guests from a pool of 40 guests is given by the combination formula:
40C2=40!2!×(40−2)!=40×392×1^{40}C_2 = \frac{40!}{2! \times (40-2)!} = \frac{40 \times 39}{2 \times 1}
Calculating this value:
40C2=20×39=780^{40}C_2 = 20 \times 39 = 780

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.

Related Comparison Tables

Permutations vs Combinations: The Quantitative Aptitude Guide

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