Question

In Super 30 movie, Anand sir asks every of 30 students to do handshake among themselves, find total number of handshakes.

• A. 435
• B. 415
• C. 600
• D. None of the above

Hint:

For any "handshake" or "matching" problem where order doesn't matter, just use the formula \( \frac{n(n-1)}{2} \).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
A handshake occurs between two people. Since the order in which two people shake hands does not matter (A shaking hands with B is the same as B shaking hands with A), this is a problem of combinations.

Step 2: Key Formula or Approach:
The number of ways to choose 2 people out of $n$ is given by the combination formula: \[ ^nC_2 = \frac{n(n-1)}{2} \]

Step 3: Detailed Explanation:
1. Here, the number of students $n = 30$. 2. To form one handshake, we need to select any 2 students out of 30. 3. Total Handshakes = $^{30}C_2$. \[ \frac{30 \times (30 - 1)}{2} = \frac{30 \times 29}{2} \] 4. Simplify the calculation: \[ 15 \times 29 = 435. \]

Step 4: Final Answer:
The total number of handshakes is 435.