Here are the questions for the first M362K homework.
Please turn in your answers in class on Thursday, Jan 29 2015.

1. How many different letter arrangements can be made from the letters
       MISSISSIPPI ?

2. A child has 12 blocks, of which 6 are black, 4 are red, 1 is white,
   and 1 is blue. If the child puts the blocks in a line, how many arrangements
   are possible?

3. In how many ways can 3 novels, 2 mathematics books, and 1 chemistry book be
   arranged on a bookshelf if
(a) the books can be arranged in any order?
(b) the math books must be together and the the novels must be together?
(c) the novels must be together, but the other books can be arranged in any order?

4. If 12 people are to be divided into 3 committees of respective
   sizes 3, 4, and 5, how many divisions are possible?

5. Consider the set of numbers { 1, 2, 3, ..., n } . 
(a) How many subsets of cardinality  k  are there?
(b) How many of those subsets have the number  i  as their highest-number?
(c) Use these observations to prove "Fermat's Identity":
                _  
     (  n  )   \   ( i-1 )
     (     ) =  >  (     )
     (  k  )   /_  ( k-1 )
               i=1