Q: 20 students are to choose a president and vice president from among themselves. How many possible ways can they be chosen?
Explanation 1: Using the Counting Principle, set up two blanks to represent the president and vice president, from left to right:
There are 20 choices for the president. Put 20 in the first blank:
The same person cannot be chosen for both positions, so there are 19 left to choose from for the vice president. Put 19 in the second blank:
Now, multiply these numbers. 20 x 19 = 380.
Explanation 2: This is a permutation problem since you are choosing 2 people from a total of 20 people, and the order is important. The order is important because the two people chosen must be given specific positions, and switching those positions results in a different scenario. Do 20 nPr 2 , or use the formula for nPr. On the TI-84 Plus, find nPr in MATH-PRB-2. The result is 380.