Question 892395
(a) A student is asked to answer 11 out of 13 questions on a exam. In how many
ways can she select the questions to be answered?(Order is not important). 
<pre>
C(13,11) = C(13,13-11) = C(13,2) = {{{13*12/(2*1)}}} = {{{156/2}}} = 78
</pre>
(b) In how many ways can a chairperson and a vice chairperson be selected from a
committee of 15 senators? 
<pre>
P(15,2) = 15*14 = 210 
</pre>
(c)How many permutations are there of the following word?
COMBINATORICS
<pre>
If the 2 C's, the 2 I's, and the 2 O's were distinguishable, the answer would be
P(13,13) = 13! since it is a 13-letter word.  However since they are not
distinguishable, we must divide by the factorial of each:

{{{13!/(2!2!2!)}}} = {{{(13*12*11*10*9*8*7*6*5*4*3*2*1)/((2*1)(2*1))}}} = 778377600   
</pre>
(d) Tarot cards are used for telling fortunes, and in a reading, the arrangement
of the cards is as important as the cards themselves. How many different
readings are possible if four cards are selected from a set of eight Tarot
cards?
<pre>
P(8,4) = 8*7*6*5 = 1680 
</pre> 
(E)A state's license plate consist of four letters followed by three numerals,
and 246 letter arrangements are not allowed. How many plates can the state
issue?
<pre>
The number of possible letter arrangement, allowed or not, are
26*26*26*26 = 26<sup>4</sup> = 11881376
[Notice that permutations do not work because we can use each letter more than
once.]
From that we subtract the 246 arrangements which are not allowed.
That's 11881376-246 = 11881130
The number of digit arrangements is 10*10*10 = 10<sup>3</sup>.
[Again permutations do not work because we can use the same digits more 
than once. 
So we multiply them tobether and get 11881376*1000 = 11881376000.

Edwin</pre>