Final answer:
In a class of 17 students, it would take 136 handshakes for everyone to shake hands with each other once. This is calculated using the combination formula: n(n-1)/2.
Step-by-step explanation:
The question is asking for the number of handshakes it would take for each student in a class of 17 students to shake hands with every other student exactly once. This is a classic problem that can be solved using the formula for the sum of the first (n-1) positive integers, where 'n' is the number of students. The formula for this scenario is n(n-1)/2.
To find the answer, we plug 17 into the formula:
Number of handshakes = 17(17-1) / 2
Number of handshakes = 17(16) / 2
Number of handshakes = 272 / 2
Number of handshakes = 136
Therefore, it would take 136 handshakes for everyone in the class to shake hands with each other once.