Lupe had a difficult time during her last group discussion. She knew her topic, but she got confused as others were talking, especially when the discussion took an unexpected direction. If the situation happens again in future group discussions, Lupe should

⊕listen carefully, take notes, and wait to share her ideas at the next discussion.
⊕learn about the ideas others are sharing so that she can find evidence right away.
⊕listen for a connection she can make, collect her thoughts, and speak clearly.
⊕try to finish someone else's thought to see his or her reaction.

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.