Need help bad, please

Question

A bag contains five batteries, all of which are the same size and are equally likely to be selected. Each battery is a different brand. If you select two batteries at random, use the counting principle to determine how many points will be in the sample space if the batteries are selected    

 

a. with replacement

b. without replacement

Answer 1

For the second problem, (b), you can use the permutation formula. This gives the number of ways of arranging n objects if r elements are selected. In this case, order is important. It is given by:

 

nPr = n!/(n-r)!

 

For this problem, n = 5, and r = 2

 

Thus, 5P2 = 5!/(5-2)!

 

               = (5 x 4 x 3 x 2 x 1)/(3 x 2 x 1)

 

               = 20 ways.

Answer 2

The counting principle says if there are m ways to do one thing

and n ways do do another, then there are m*n ways of doing both.

 

a. 5 ways to grab first battery;  put battery back;

    5 ways to grab second battery

  = 25 ways in the sample space.

 

b. 5 ways to grab first battery; DON'T put battery back;

    4 ways to grab second battery
= 20 ways in the sample space.