Counting

How many ways are there for Pamela to get from home to school? She can only move in the directions given by the arrows (right and up).

Elijah is thinking of a password for his game account. In order to make it more complicated, he decides to use 2 digits (any digit from 0 to 9) followed by an alphabet from his name where upper case and lower case are considered to be different. For example, 000a and 000A are different passwords. How many possible passwords can he have?

There are 3 roads from Town A to Town B, 5 roads from Town B to Town C, and 4 roads from Town A to Town C. How many different ways are there to go from Town A to Town C?

There are 3 roads from Town A to Town B, 5 roads from Town B to Town C, and 4 roads from Town A to Town C. How many ways are there to go from Town B to Town C?

Using the digits 1, 2, 3, 4 and 5, how many 4-digit numbers can be used if each digit may only be used once?

Using the digits 1, 2, 3, 4 and 5, how many 4-digit even numbers can be used if each digit may only be used once?

Using the digits 1, 2, 3, 4 and 5, how many 4-digit odd numbers can be used if each digit may only be used once?

John's class has 25 students. Two students need to be selected such that one is the Class Monitor and one is the Assistant Class Monitor. How many different selections are there?

John's class has 25 students. Two students need to be selected to represent the class in a Wai Khru ceremony. How many different selections are there?

Andrew's class has 20 students. Three students need to be selected such that one is the Math representative, one is the English representative and one is the Science representative. How many ways are there?