To find the total number of handshakes when each student shakes hands with every other student exactly once, we can use the formula for combinations:
Number of handshakes=(n2)=n×(n−1)2\text{Number of handshakes}=\binom{n}{2}=\frac{n\times (n-1)}{2}Number of handshakes=(2n)=2n×(n−1)
where nnn is the number of students. Here, n=8n=8n=8. So,
Number of handshakes=8×(8−1)2=8×72=562=28\text{Number of handshakes}=\frac{8\times (8-1)}{2}=\frac{8\times 7}{2}=\frac{56}{2}=28Number of handshakes=28×(8−1)=28×7=256=28
Answer: There are 28 handshakes altogether.
