SOLUTION: This is the new girl calling for help again please A specific brand of bike comes in two frames, for males or females. Each frame comes in a choice of three colors, red, wh

Question 199872: This is the new girl calling for help again please

A specific brand of bike comes in two frames, for males or females. Each frame comes in a choice of three colors, red, white, and blue, and with a choice of three seats, soft, medium, and hard.
a) Use the counting principle to determine the number of different arrangements of bicycles that are possible.
b) Construct a tree diagram illustrating all the different arrangements of bicycles that are possible.
c) List the sample space.

Thank you T-Aun

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a)

Number of Genders * Number of Colors * Number of Seat Choices = 2 * 3 * 3 = 6 * 3 = 18

So there are 18 different bike configurations.

b)

Here's the tree diagram:

c)

Here are ALL of the possible configurations which form the sample space:

{male, red, soft}
{male, red, medium}
{male, red, hard}
{male, white, soft}
{male, white, medium}
{male, white, hard}
{male, blue, soft}
{male, blue, medium}
{male, blue, hard}
{female, red, soft}
{female, red, medium}
{female, red, hard}
{female, white, soft}
{female, white, medium}
{female, white, hard}
{female, blue, soft}
{female, blue, medium}
{female, blue, hard}

Note: an example point {female, red, soft} means that the bike has a female frame, is red, and has a soft seat.
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