Combinations
A team has 12 players: 6 boys and 6 girls. Coach wants to pick a group of 5 students: 3 boys and 2 girls. How many ways can Coach select this group.
20*15=300
There are 6 Germans, 5 French, and 3 Italians at a meeting. How many ways are there for everyone to sit in a row if people from the same country must sit together?
6! * 5! * 3! * 3!
Find the probability that a randomly selected card from a deck of cards will be a number card (2-10).
36/52 = 9/13
How many positive integers are there less than 1000 such that the digits are in strictly increasing order?
129
How many ways to get from the bottom left to the top right of a 4x5 grid in 9 steps?
126
I draw 2 cards from a standard deck of cards. Find the probability that they are both the same color.
25/51
A number is a mountain number if the middle digit is strictly larger than any of the other digits. How many 3-digit numbers are mountain numbers?
240
How many sequences of 6 digits can we form such that no 2 adjacent digits have the same parity (no two adjacent digits are both even and no two adjacent digits are both odd)?
P(Heads) = 1/3
P(Tails) = 2/3
Find the probability that I flip exactly 3 Tails from 5 coin flips.
80/243