Problem 15E

A combination lock requires three selections of numbers, each from 1 through 30.

a. How many different combinations are possible?

b. Suppose the locks are constructed in such a way that no number may be used twice. How many different combinations are possible?

MODULE 15 -- BASIC COUNTING, PERMUTATIONS → 6.1 BASIC COUNTING ← The Product Rule: A procedure can be broken down into a sequence of two tasks. There are n w1ys to do the first task and n ways2to do the second task. Then there are n 1n 2ays to do the procedure. Example: How many bit strings of length seven are there 7 Solution: Since each of the seven bits is either a 0 or 1, the answer is 2 = 128. Example: How many different license plates can be made if each plate contains a sequence of three uppercase English letters followed by three digits Solution: Using the product rule, there are 26 • 26 • 26 • 10 • 10 • 10 = 17,576,000 different possible license plates. 26 represents the 26 choices for eac