math question

Question

A School district is going to hire a soccer coach and assistant coah. In how many different ways can the selection be made if 18 equally qualified people apply for the positions?

Answer 1

We want to select one coach and one assistant coach from a group of 18 people.

There are 18P2 ways to make this selection.

Number of ways = 18P2 = 306

Answer 2

Hi Heather,

 

http://www.mathplanet.com/education/pre-algebra/probability-and-statistic/combinations-and-permutations

 

http://www.mathsisfun.com/combinatorics/combinations-permutations.html

 

N would be 18 and r would be 2.

 

Permutations with Repetition

These are the easiest to calculate.

When we have n things to choose from ... we have n choices each time!

When choosing r of them, the permutations are:

n × n × ... (r times)

(In other words, there are n possibilities for the first choice, THEN there are n possibilites for the second choice, and so on, multplying each time.)

Which is easier to write down using an exponent of r:

n × n × ... (r times) = nr

Example: in the lock above, there are 10 numbers to choose from (0,1,...9) and we choose 3 of them:
10 × 10 × ... (3 times) = 103 = 1,000 permutations

 

Jim Gibbs