The Cupcake Spot made 136 cupcakes: there are 36 chocolate flavored, 52 red velvet flavored and the rest are vanilla flavored cupcakes. The bakery wants to mix and package the cupcakes so that each box has the same number of cupcakes in each box. How many boxes are there at most? How many of each flavor is in each of the boxes?

Daniel bought a computer game for $25 and later sold it to thomas for a 40% profit. how much did daniel sell the computer game for?

Alicia puts $400 in a bank account. each year the account earns 5% simple interest. how much money will be in her bank account in six months?

Suppose we have a set of small wooden blocks showing the 26 letters of the english alphabet, one letter per block. (think of scrabble tiles.) our set includes 10 copies of each letter. we place them into a bag and draw out one block at a time. (a) if we line up the letters on a rack as we draw them, how different ways coukl we fill a rack of 5 letters? (b) now suppose we just toss our chosen blocks into a pile, and whenever we draw a letter we already have, we put it back in the bag and draw again. how many different piles of 5 blocks could result? possible? piles will contain at least one repeated letter? (c) if we draw out 5 blocks wit hout looking at them, how many different piles are (d) if we draw out 5 blocks without looking at them, how many of the possible 2. (4) consider the following formula. 12 give two different proofs, one using the factorial formulas and the other combina torial.