Counting Basics
How many 4-digit numbers have digits in strictly increasing order?
126
How many permutations of the letters in BALLOON exist?
1260
How many subsets of {1,2,3,4,5} contain at least one even number?
24
Three coins flipped. Probability of exactly two heads?
3/8
How many positive integers ≤1000 are divisible by 4 or 6?
333
How many 7-digit numbers use digits 1–7 exactly once and have 1 somewhere before 2?
2520
How many solutions to x+y+z=7x+y+z=7x+y+z=7 in nonnegative integers?
36
Two cards drawn without replacement. Probability both are aces?
1/221