Question 767241: The letters A,B,C,D and E are arranged in random order.
(a)What is the probability that the three letters
A,B,and C appear in this particular order somewhere in the string of letters?
(b) What is the probability that the letters A,B,and C appear in anyorder (i.e.
ABC,CBA,BCA
etc.)somewhere in the string of letters?
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website! The letters A,B,C,D and E are arranged in random order.
(a)What is the probability that the three letters
A,B,and C appear in this particular order somewhere in the string of letters?
They can appear like this
A,B,C,_,_ in 2 ways, ABCDE and ABCED
_,A,B,C,_ in 2 ways, DABCE and EABCD
_,_,A,B,C in 2 ways, DEABC and EDABC
That's 6 ways out of 5! or  =  =  = 0.05 = 5% of the time that will happen.
(b) What is the probability that the letters A,B,and C appear in any order (i.e.
ABC,CBA,BCA etc.)somewhere in the string of letters?
There are 3! times as many ways as in part (a), each order the same as A,B,C
That's 3!×6 or 6×6=36 ways out of 5! or  =  =  = 0.30 = 30% of the time that will happen.
Edwin
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