Question

If two states are selected at random from a group of 50 ​states, determine the number of possible outcomes if the group of states are selected with replacement

Answer 1

Since the order of selected ways doesn't matter, this is a combination of 2 items chosen among the 50: 
⁵⁰c₂ = (50!)/(50-2)!.(2!) = 1225 ways

Answer 2

Answer:

The are 1225 possible outcomes.

Step-by-step explanation:

The order of the states do not matter. For example, New York and California is the same outcome as California and New York. This means that we use the combination formula to solve this problem.

Combination formula

$C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$.

In this problem, we have that:

Two states are selected at random from a group of 50 ​states. This means that we have a combination of 2 states from a set of 50 states. So we have that $n = 50, x = 2$.

$C_{50,2} = \frac{50!}{2!(48)!} = 1225$

The are 1225 possible outcomes.