If you're on this app, it probably means you struggle in academics. That's okay! It doesn't make you dumb or anything like that. It means you struggle in something. It doesn't make you less than Bethany over there complaining about the 90 she got on her quiz, I'm sue she struggles just as much in another area you're incredible at! You might be a great painter or a great musical artist, but there's something you're good at. There has to be. A person as incredible as you has to be great at s many things! Pick your chin up sovereign, your crown's tipping.

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.