27.)There are 30 future project managers in exam center.If all shake hands with one another how many handshakes are possible? a. 900 a. 870 a. 660 b. 435

To find the number of handshakes possible if each person shakes hands with every other person, we can use the formula for combinations:<br /><br />\[<br />\text{Number of handshakes} = \binom{n}{2} = \frac{n(n-1)}{2}<br />\]<br /><br />where \( n \) is the total number of people. In this case, \( n = 30 \).<br /><br />\[<br />\text{Number of handshakes} = \frac{30 \times 29}{2} = \frac{870}{2} = 435<br />\]<br /><br />Therefore, the correct answer is:<br /><br />b. 435