(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?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2. (а)
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?
Transcribed Image Text:2. (а) 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?
Expert Solution
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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