A puzzle in the newspaper presents a matching problem. The names of 10 U.S. presidents are listed in one column, and their vice presidents are listed in random order in the second column. The puzzle asks the reader to match each president with his vice president.
(1) If you make the matches randomly, how many matches are possible?
Number of possible matches
(2) What is the probability all 10 of your matches are correct? (Round your answer to 8 decimal places.)

We are given that a puzzle in the newspaper presents a matching problem. The names of 10 U.S. presidents are listed in one column, and their vice presidents are listed in random order in the second column.

(1) If we make the matches randomly, number of possible matches are given by = 10!

Because after making each match the number will decrease so,

Number of possible matches = 10! = 10*9*8*7*6*5*4*3*2*1 = 3628800 .

(2) The probability all 10 of your matches are correct is given by;

Number of outcomes in favor ÷ Total number of matches

So, there will be only 1 case when all 10 of the matches are correct.

Therefore, required probability = [tex]\frac{1}{10!}[/tex] = [tex]\frac{1}{3628800}[/tex] = 0.00000028 .