(a) Suppose a code consists of five characters, three digits followed by two letters. Find the number of: i. codes ii. codes with distinct letters iii. codes with distinct digits. (b) Josh wants to go to Sacramento. He can choose from 4 bus services or 3 train services to head from home to downtown LA. From there, he can choose from 5 bus services or 4 train services to head to Sacramento. How many ways are there for Josh to get to Sacramento?
(a) Suppose a code consists of five characters, three digits followed by two letters. Find the number of: i. codes ii. codes with distinct letters iii. codes with distinct digits. (b) Josh wants to go to Sacramento. He can choose from 4 bus services or 3 train services to head from home to downtown LA. From there, he can choose from 5 bus services or 4 train services to head to Sacramento. How many ways are there for Josh to get to Sacramento?
Chapter9: Sequences, Probability And Counting Theory
Section: Chapter Questions
Problem 17PT: A buyer of a new sedan can custom order the car by choosing from 5 different exterior colors, 3...
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Step 1
The concept used is the product rule:
If there are n ways to do task A and m ways to do task B, then the number of ways to do A and B together is nm.
The above is true if the number of ways of doing A and B is independent; and that the number of choices for doing B is the same regardless of the choice for A.
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