Counting & Probability

Counting Basics

100

How many 4-digit numbers have digits in strictly increasing order?

126

200

How many positive integers ≤1000 are divisible by 4 or 6?

333

Permutations with Restrictions

100

How many permutations of the letters in BALLOON exist?

1260

200

How many 7-digit numbers use digits 1–7 exactly once and have 1 somewhere before 2?

2520

Combinatorics / Selection

100

How many subsets of {1,2,3,4,5} contain at least one even number?

24

200

How many solutions to x+y+z=7x+y+z=7x+y+z=7 in nonnegative integers?

36

Probability

100

Three coins flipped. Probability of exactly two heads?

3/8

200

Two cards drawn without replacement. Probability both are aces?

1/221