if you have 8 pennies in your pocket, and you pull the coins out of your pocket 1 at a time, what is the probablility that they are taken out in order by date.

Question

if you have 8 pennies in your pocket dated, 1972, 1978, 1979, 1985, 1989, 1991, 1993, and 1995. if you take the coins out of your pocket 1 at a time,  what is the probablility that they are taken out in order by date.

Answer 1

The chance that you pull out the 1972 penny is 1/8.  After that, there are 7 pennies left.  Given 7 pennies, the chance that you pull out the 1978 penny is 1/7.  This chain of reasoning continues until you are have 1 penny left.  The chance of pulling that last penny is 1, since it is the only penny to pull.

 

Putting this all together yields the probability

 

(1/8)*(1/7)*...*(1/2)*1

=1/8!