<PRE><B>Question 1206342</B>
&lt;font color=black size=3&gt;
Answers:
(a) &lt;font color=red size=4&gt;21&lt;/font&gt;
(b) &lt;font color=red size=4&gt;72&lt;/font&gt;


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Explanation for part (a)


Break things up into three cases:
(1) Exactly zero &#39;E&#39;s are chosen
(2) Exactly one &#39;E&#39; is chosen
(3) Exactly two &#39;E&#39;s are chosen


Case (1)
The letters to pick from are {S,L,C,T}
There are 4*3 = 12 different two letter words possible where &quot;E&quot; isn&#39;t chosen.
Alternatively, you can use the nPr permutation formula with n = 4 and r = 2.
Of course when I say &quot;word&quot;, I mean it in quotes because much of these two-letter strings aren&#39;t words found in the dictionary.
An example word of case (1) would be SL.


Case (2)
Let&#39;s say &quot;E&quot; is in the first slot. There would be 4 words we can form which are: ES, EL, EC, ET
We will also have 4 words with &quot;E&quot; in the second slot.
That&#39;s 4+4 = 8 different words that have exactly one &quot;E&quot;.
An example word of case (2) would be SE.


Case (3)
This is a trivial case of just one possibility. The word EE.


Add up the results:
12+8+1 = &lt;font color=red&gt;21&lt;/font&gt; is the final answer to part (a)


Here is the list of all 21 unique entries (7 rows, 3 columns)
&lt;table border = &quot;1&quot; cellpadding = &quot;5&quot;&gt;&lt;tr&gt;&lt;td&gt;1&lt;/td&gt;&lt;td&gt;SE&lt;/td&gt;&lt;td&gt;SL&lt;/td&gt;&lt;td&gt;SC&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;2&lt;/td&gt;&lt;td&gt;ST&lt;/td&gt;&lt;td&gt;ES&lt;/td&gt;&lt;td&gt;EL&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;3&lt;/td&gt;&lt;td&gt;EE&lt;/td&gt;&lt;td&gt;EC&lt;/td&gt;&lt;td&gt;ET&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;4&lt;/td&gt;&lt;td&gt;LS&lt;/td&gt;&lt;td&gt;LE&lt;/td&gt;&lt;td&gt;LC&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;5&lt;/td&gt;&lt;td&gt;LT&lt;/td&gt;&lt;td&gt;CS&lt;/td&gt;&lt;td&gt;CE&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;6&lt;/td&gt;&lt;td&gt;CL&lt;/td&gt;&lt;td&gt;CT&lt;/td&gt;&lt;td&gt;TS&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;7&lt;/td&gt;&lt;td&gt;TE&lt;/td&gt;&lt;td&gt;TL&lt;/td&gt;&lt;td&gt;TC&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;
The list was generated using this combinatorics calculator
&lt;a href=&quot;https://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html&quot;&gt;https://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html&lt;/a&gt;



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Explanation for part (b)


We&#39;ll have three cases:
Case (1): Exactly 0 &#39;E&#39;s are chosen
Case (2): Exactly 1 &#39;E&#39; is chosen
Case (3): Exactly 2 &#39;E&#39;s are chosen
We stop here since we cannot select 3 &quot;E&quot;s.


Case (1)
There are 4 items to pick from in the set {S,L,C,T}
That gives 4*3*2 = 24 ways to form a three-letter word without any &quot;E&quot;s in it.
An example word of case (1) would be SLC.


Case (2)
We have 3 places to put the &quot;E&quot;.
Then we have 4*3 = 12 ways to pick the other letters where order matters.
3*12 = 36 ways to form a three-letter word with exactly one &quot;E&quot; in it.
An example word of case (2) would be SEL.


Case (3)
There are 3 slots to choose from for one of these letters {S,L,C,T}
3*4 = 12 ways to form a three-letter word with exactly two &quot;E&quot;s in it.
An example word of case (3) would be SEE.


Add up the results:
24+36+12 = &lt;font color=red&gt;72&lt;/font&gt; is the final answer to part (b)


Below is the list of all 72 unique entries.
The list was generated with the previously mentioned link.
The table has 9 rows and 8 columns.
&lt;table border = &quot;1&quot; cellpadding = &quot;5&quot;&gt;&lt;tr&gt;&lt;td&gt;&lt;/td&gt;&lt;td&gt;1&lt;/td&gt;&lt;td&gt;2&lt;/td&gt;&lt;td&gt;3&lt;/td&gt;&lt;td&gt;4&lt;/td&gt;&lt;td&gt;5&lt;/td&gt;&lt;td&gt;6&lt;/td&gt;&lt;td&gt;7&lt;/td&gt;&lt;td&gt;8&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;1&lt;/td&gt;&lt;td&gt;SEL&lt;/td&gt;&lt;td&gt;SEE&lt;/td&gt;&lt;td&gt;SEC&lt;/td&gt;&lt;td&gt;SET&lt;/td&gt;&lt;td&gt;SLE&lt;/td&gt;&lt;td&gt;SLC&lt;/td&gt;&lt;td&gt;SLT&lt;/td&gt;&lt;td&gt;SCE&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;2&lt;/td&gt;&lt;td&gt;SCL&lt;/td&gt;&lt;td&gt;SCT&lt;/td&gt;&lt;td&gt;STE&lt;/td&gt;&lt;td&gt;STL&lt;/td&gt;&lt;td&gt;STC&lt;/td&gt;&lt;td&gt;ESL&lt;/td&gt;&lt;td&gt;ESE&lt;/td&gt;&lt;td&gt;ESC&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;3&lt;/td&gt;&lt;td&gt;EST&lt;/td&gt;&lt;td&gt;ELS&lt;/td&gt;&lt;td&gt;ELE&lt;/td&gt;&lt;td&gt;ELC&lt;/td&gt;&lt;td&gt;ELT&lt;/td&gt;&lt;td&gt;EES&lt;/td&gt;&lt;td&gt;EEL&lt;/td&gt;&lt;td&gt;EEC&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;4&lt;/td&gt;&lt;td&gt;EET&lt;/td&gt;&lt;td&gt;ECS&lt;/td&gt;&lt;td&gt;ECL&lt;/td&gt;&lt;td&gt;ECE&lt;/td&gt;&lt;td&gt;ECT&lt;/td&gt;&lt;td&gt;ETS&lt;/td&gt;&lt;td&gt;ETL&lt;/td&gt;&lt;td&gt;ETE&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;5&lt;/td&gt;&lt;td&gt;ETC&lt;/td&gt;&lt;td&gt;LSE&lt;/td&gt;&lt;td&gt;LSC&lt;/td&gt;&lt;td&gt;LST&lt;/td&gt;&lt;td&gt;LES&lt;/td&gt;&lt;td&gt;LEE&lt;/td&gt;&lt;td&gt;LEC&lt;/td&gt;&lt;td&gt;LET&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;6&lt;/td&gt;&lt;td&gt;LCS&lt;/td&gt;&lt;td&gt;LCE&lt;/td&gt;&lt;td&gt;LCT&lt;/td&gt;&lt;td&gt;LTS&lt;/td&gt;&lt;td&gt;LTE&lt;/td&gt;&lt;td&gt;LTC&lt;/td&gt;&lt;td&gt;CSE&lt;/td&gt;&lt;td&gt;CSL&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;7&lt;/td&gt;&lt;td&gt;CST&lt;/td&gt;&lt;td&gt;CES&lt;/td&gt;&lt;td&gt;CEL&lt;/td&gt;&lt;td&gt;CEE&lt;/td&gt;&lt;td&gt;CET&lt;/td&gt;&lt;td&gt;CLS&lt;/td&gt;&lt;td&gt;CLE&lt;/td&gt;&lt;td&gt;CLT&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;8&lt;/td&gt;&lt;td&gt;CTS&lt;/td&gt;&lt;td&gt;CTE&lt;/td&gt;&lt;td&gt;CTL&lt;/td&gt;&lt;td&gt;TSE&lt;/td&gt;&lt;td&gt;TSL&lt;/td&gt;&lt;td&gt;TSC&lt;/td&gt;&lt;td&gt;TES&lt;/td&gt;&lt;td&gt;TEL&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;9&lt;/td&gt;&lt;td&gt;TEE&lt;/td&gt;&lt;td&gt;TEC&lt;/td&gt;&lt;td&gt;TLS&lt;/td&gt;&lt;td&gt;TLE&lt;/td&gt;&lt;td&gt;TLC&lt;/td&gt;&lt;td&gt;TCS&lt;/td&gt;&lt;td&gt;TCE&lt;/td&gt;&lt;td&gt;TCL&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;
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