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?
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)
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.
`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