Combinatorics and Probability

1. A number is randomly chosen from a list of 10 consecutive positive integers. What is the probability that the number selected is greater than the average (arithmetic mean) of all 10 integers?

Reveal Answer

Say the numbers = 1, 2, 3, …, 10 → Average = 5.5 → P = 5/10 = 1/2

2. A restaurant menu has several options for tacos. There are 3 types of shells, 4 types of meat, 3 types of cheese, and 5 types of salsa. How many distinct tacos can be ordered assuming that any order contains exactly one of each of the above choices?