Question

(HELP FINAL EXAM) 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 replacement or without replacement.

Answer 1

With replacement, there are 1600 possible outcomes.

Without replacement, there are 1560 possible outcomes.

Explanation:

Chosen with replacement:

State is chosen, then put back in the group, then another state can be chosen. In both cases, there will be 40 possible outcomes, as the first taken state is placed back. So

40*40 = 1600

With replacement, there are 1600 possible outcomes.

Chosen without replacement:

State and chosen and is not replaced.

So, for the second state, there will be only 39 possible outcomes.

40*39 = 1560

Without replacement, there are 1560 possible outcomes.