If two states are selected at random from a group of 20 states, determine the number of possible outcomes if the group of states are selected with replacement or without replacement.

With replacement

 21C2 = 210 outcomes

without replacement

20C2 = 190 outcomes

Step-by-step explanation:

For determining the number of possible outcomes you need count the number of possible combinations, because a combination is a selection of a number of items from a set of items where the order of selection does not matter.

The number of possible combinations is calculated thus

nCr =

     

           Where n: number of items of the set

                        r: number of selected items

a) If the group of states are selected with replacement then

   (n+r-1)Cr  

   n = 20 states

   r = 2 states

  then n +r -1 = 20 +2 -1 = 21

  21C2 =

b) If the group of states are selected without replacement then

 nCr

 n = 20

 r = 2

20C2 =

   

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