Question

Fifteen participants for the MTAP competition were asked to shake hands and introduce themselves with each other. How many hands hakes took place?

A. 15
B. 30
C. 45
D. 105

Answer 1

To calculate the number of handshakes at the MTAP competition with 15 participants, we use the combination formula, resulting in a total of 105 handshakes.

Step-by-step explanation:

The MTAP competition question is a classic example of a combinatorial problem in mathematics where one seeks to find the number of distinct pairs that can be formed from a set of items. In this case, the number of handshakes can be found using the combination formula for pairs, which is n(n-1)/2 where n is the number of participants.

For 15 participants, the formula becomes 15(15-1)/2 = 15×14/2 = 105. Therefore, the total number of handshakes made is 105. The correct answer to the question is D. 105.