there are 6 contestants for the post of chairman

Question

There are 6 contestants for the post of chairman secretary and treasurer. These positions can be filled by any of the 6. Find the possible no. of ways whether the 3 positions may be filled.

Solution

Chairman   Secretary   Treasurer

       6             5               4

Hence the no of ways of filing the three positions is 6 x 5 x 4 = 120

⁶P₃ =   (6!)/((6 - 3)! )  

= (6 * 5 * 4 * 3 * 2 * 1) /(3 * 2 * 1)

= 720/6

= 120