How can five candies be distributed among 3 friends? Well, the answer depends on if you can tell the candies apart!
There are 5 stars and 4 bars to be arranged in the 9 spaces pictured below. One possible arrangement is shown.
How many possible arrangements are there?
Find the number of positive integer solutions of the equation
\[x + y + z = 12.\]
Find the number of 8-digit numbers the sum whose digits is 4.
How many (positive) seven digit integers are there that have a digit sum equal to \(10\) and that are formed using only the digits \(1\), \(2\) and \(3\)?
There are 20 distinct people signed up for a raffle. There are 3 prizes that can be won: a 100 cm HDTV, a signed football jersey, and an envelope filled with gift cards. It is possible for a person to win more than one prize.
How many possible prize distributions are there?