# Hello, I am in 6th grade and I am having some trouble with my math homework. Right now, we are learning about sample spaces. The problems I'm having trouble on are: 1) There are 5 ways to go from...

Hello, I am in 6th grade and I am having some trouble with my math homework. Right now, we are learning about sample spaces. The problems I'm having trouble on are:

1) There are 5 ways to go from Town X to Town Y. There are 3 ways to go from Town Y to Town Z. How many different wys are there to go from Town X to Town Z, passing through Town Y?

and

2) Rasheed has tan pants, black pants, gray pants, and blue pants. He has a brown sweater and a white sweater. How many different ways can he wear a sweater and pants together?

Your help will be greatly appreciated!!!

Thank you, NoName (my nickname)

violy | Certified Educator

We will apply Fundamental Counting Principles here. When there are m ways to do one thing, and n ways to do another, then there are m×n ways of doing both.

So, for the number of different ways from X to Z we will have:

5*3 = 15 ways

Same principle applies for number 2.

There are 3 different pants, and 2 different sweaters.

So, we will have 3 * 2 = 6 ways to wear sweaters and pants together.

oldnick | Student

`1)` For every way you use to go from X to Y  you can use one of the way to go  from Y to Z so for 5 ways   `X---> Y`  can choice  3 ways

`Y-------->Z`  for a total of  `3xx5= 15 ways`

`2)`  The reasonement is the same of 1).

Indeed for every pant  you can use one sweater,  since the pants are 3 andthe sweater 2 , then can  use togeter `3xx2=6`  couple