Question

If two states are selected at random from a group of 40 states, determine the number of possible outcomes if the group of states are selected with replaceme without replacement If the states are selected with replacement, there are 1600 possible outcomes. If the states are selected without replacement, there arepossible utcomes.

Answer 1

The number of possible outcomes when selecting two states without replacement from a group of 40 states is 780.

Step-by-step explanation:

The question is asking how many possible outcomes there are when two states are selected from a group of 40 states. When selecting with replacement, meaning a state can be selected more than once, the number of possible outcomes is 40 times 40, which equals 1600. When selecting without replacement, meaning each state can only be selected once, we use the formula for combinations because the order of selection does not matter. The number of possible outcomes without replacement is calculated as 40 choose 2, which uses the combination formula C(n, k) = n! / (k!(n - k)!), where n is the total number of items, k is the number of items to choose, and ! denotes factorial.

For our case, C(40, 2) = 40! / (2!(40 - 2)!) = (40 × 39) / (2 × 1) = 780. Therefore, there are 780 possible outcomes when two states are selected from a group of 40 states without replacement.