SAT – Counting and Ordering

Q:  20 students are to choose a president and vice president from among themselves. How many possible ways can they be chosen?

Answer:  380

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:

_20_    ____

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:

_20_    _19_

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.

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SAT – Counting and Ordering

Q: In how many ways can the letters of the word ‘FIVE’ be arranged?

Answer:   24

Explanation 1:  SInce there are 4 different letters, do 4!  (that’s ‘4 factorial’).   4! = 4 x 3x 2x 1 = 24.  Your calculator might have a factorial (!) function.  On the TI-84 Plus, find it in MATH – PRB.

Explanation 2:  SInce you are choosing 4 items from a total of 4 items, and the order is important, you can do 4 nPr 4, or use the formula for nPr.

 

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