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?
<pre>
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 {{{6/5!}}} = {{{6/120}}} = {{{1/20}}} = 0.05 = 5% of the time that will happen.
</pre> 
(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?
<pre>
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 {{{36/5!}}} = {{{36/120}}} = {{{3/10}}} = 0.30 = 30% of the time that will happen.

Edwin</pre>