24 1. Let’s Count!
1.8.29What is the number of ways to colornobjects with 3 colors if every
color must be used at least once?
1.8.30Draw a tree for Alice’s solution of enumerating the number of ways 6
people can play chess, and explain Alice’s argument using the tree.
1.8.31How many different “words” can you get by rearranging the letters in
the word MATHEMATICS?
1.8.32Find all positive integersa,b, andcfor which
a
b
b
c
=2
a
c
.1.8.33Prove that
n
k
=
n− 2
k
+2
n− 2
k− 1
+
n− 2
k− 2
.1.8.3420 persons are sitting around a table. How many ways can we choose 3
persons, no two of whom are neighbors?