MC 36
Fall 1998
Problem Set 1
Due 9/21/98
 
  1. Grimaldi 1.1/1.2:  4,6,22,34
  2. Grimaldi 1.3:  6,8,12,14,20
  3. Grimaldi 1.4:  4,8,12
  4. How many permutations of the letters a,b, ..., g contain either two or three letters between a and b (a can appear before or after b)?
  5. How many subsets of a set with 10 elements are there?
  6. How many subsets with an odd number of elements does a set with 10 elements have?
  7. In how many ways can ten adults and five children stand in a circle so that no two children are next to each other?
  8. Give a combinatorial proof that 
            n
            \                                  n-1
            /_    k  C(n,k) = n  2
          k=1

(Hint:  Count in two ways the number of ways to select a committee with a leader of the committee.)