"Published in Newark, California, USA"
If polygons are labeled by placing letters at their vertices, how many ways are there of labeling (a) a triangle, (b) a quadrilateral, (c) a hexagon with the first 10 letters of the alphabet?
Solution:
The given word problem above is about permutations. Permutation is an arrangement of a number of objects in a definite order. To "permute" a set of objects means to arrange them in a definite order. The number of permutations of n things taken r at a time is given by the formula
where n! (read as n factorial) is equal to n(n -1)(n - 2)......3∙2∙1. Take note that the values of n and r must be zero and positive numbers only. 0! is equal to 1.
Now, let's go back to the given problem and solve for the permutations of the given polynomials.
(a) For a triangle, the number of ways to label the vertices with the first 10 letters of the alphabet are
(b) For a quadrilateral, the number of ways to label the vertices with the first 10 letters of the alphabet are
(c) For a hexagon, the number of ways to label the vertices with the first 10 letters of the alphabet are
