Question 1205238
<pre>
The above solution is incorrect.  She took it to be choosing all 10 letters.
We are only choosing 4 of them.

We will have letters to rearrange of the following forms: 
XYZW, XXYZ, XXYY, or XXXY, where the letters X,Y,Z,W can represent
distinguishable letters of STATISTICS.  So there are 4 cases.

Case XYZW. The letters are all distinguishable. We choose any 4 from 
the 5 letters STAIC C(5,4)=5 ways and arrange them 5!=120 ways.    

Case XXYZ. 2 letters are indistinguishable. We choose the letter for 
X from the letters STI C(3,2)=3 ways and the Y and Z from the 4 letters, 
made up of the 2 letters we didn't choose for X, A and C, which is C(4,2)=6  
That's (3)(6)=18 ways, and then we can rearrange the letters {{{4!/(2!)=12}}} ways. 
That's (18)(12)=216 ways.

Case XXYY. The 2 letters for X are indistinguishable. The 2 letters for Y's 
are indistinguishable. We choose the letters X and Y from the letters STI 
C(3,2)=3 ways. Then we can rearrange the letters {{{4!/(2!2!)=6}}} ways. 
That's (3)(6)=18 ways.

Case XXXY. We can choose the S or the T for X.  That's 2 ways.  That leaves 4
ways to choose the letter for Y. That's (2)(4)=8 ways.  Then we can rearrange
the letters {{{4!/(3!)=4}}} ways. That's (8)(4)=32 ways.

Total = 120+216+18+32 = 386 ways.

Edwin</pre>