Question 855773
In the word DISCRETE how many :

1. 8 letter word can be formed
2. 7 letter word can be formed
3. 6 letter word can be formed
4. 5 letter word can be formed
<pre>
The 2 E's are indistinguishable.  So anytime we use both E's we
must divide by 2!.


1. The number of 8 letter words is {{{8!/2!}}} = 20160

2. The number of 7 letter words must be broken down into two
   cases:

   Case 1: Only one E is used: 7! = 5040
   Case 2: Both E's are used.
           We can choose the 5 other letters to use from these
           six {D,I,S,C,R,T}.  That's C(6,5) = 6 ways.
           For each of those 6 ways there are {{{7!/2!}}} = 2520
           ways to arrange them.
           So for case 2 we have 6×2520 = 15120

Total = 5040 + 15120 = 20160

3. The number of 6 letter words must also be broken down into two
   cases:
 
   Case 1: No more than 1 E is used.
           We choose the 6 letters to use from these {D,I,S,C,R,E,T}
           That's C(7,6) = 7 ways
           For each of those 7 ways there are 6! = 720 ways
           to arrange them.
           So for case 1, there are 7×720 = 5040 ways.
   Case 2: Both E's are used.
           We can choose the 4 other letters to use from these
           six {D,I,S,C,R,T}.  That's C(6,4) = 6 ways.
           For each of those 6 ways there are {{{6!/2!}}} = 360
           ways to arrange them.
           So for case 2 we have 6×360 = 2160 ways.

Total = 5040+2160 = 7200 ways.

I'll let you do the 5-letter words.

Edwin</pre>