I have 7 identical balls and 6 identical bins. How many ways can I put the balls in the bins so that every ball is inside a bin?
Mark rolls two dice. How many ways are there for the sum of the dice to be greater than 8?
A 5-letter password can use any digit less than 8. How many ways are there for the password to contain more than 2 threes?
Alice and Bob play a game. They each roll a die. If they both roll an even number, Alice wins. If they both roll an odd number, Bob wins. If neither happens, they roll again. However, if they both roll a number divisible by 3, they reroll, and the win does not count, even if they should have won according to the rules above. What is the probability that Alice wins?
I have 7 distinguishable balls and 4 identical bins. How many ways can I put the balls in the bins so that every ball is inside a bin?