Question

If two states are selected at random from the 50 u.s states, use the counting principle to determine the number of possible outcomes if the states are selected.
a)with replacement
b)without replacement

i really want to learn this its annoying me >:( :(

Answer 1

When you use replacement, each selection has the same number of options so it would 50*50

Answer 2

Lets start off with A
So for the first option there are 50 states you can choose a possibility of 50 states
Now for the second one again there is a possibility of choosing 50 states
So for there are 50*50 options

Answer 3

Without replacement, you have one less option each time so 50*49

Answer 4

but they use two states so wouldnt it be 50*48? and why are you multiplying 50*50. where do the two states come from then

Answer 5

hmmm how can we explain this

Answer 6

Umm lets start off with a simple example so that you can understand this concept

Answer 7

ok

Answer 8

You pick in two rounds. First round you pick one, put it back and then pick another one. Thus in total you picked 2

Answer 9

If two states are selected at random from the 50 u.s states, use the counting principle to determine the number of possible outcomes if the states are selected.

a)with replacement
50*50
b)without replacement
50*49

Answer 10

oh okay i get it thanks so much guys(:

Answer 11

YAY. I'm so happy for you

Answer 12

dang it forget my example :P
You already figured it out

Answer 13

thats openstudy, somebody steals your thought

Answer 14

:)

Answer 15

-.-

Answer 16

its easier to explain if we look at a reduced sample space
imagine there is only 4 states in the whole country. call it A, B, C , D

Answer 17

Yaaa thats my personal opinion so that he/she can see how this method works in a concrete manner.

Answer 18

now you have two cases.
with replacement:

so first choice you have A, B, C or D ,