You are studying for your final exam of the semester. up to this point, you received 3 exam scores of 67%, 68%, and 78℅. to receive a grade of c in the class, you must have an average exam score between 70% and 79% for all 4 exams including the final.

find the widest range of scores that you can get on the final exam in order to receive a grade of c for the class. use interval notation.

a) [70,71]
b) [62,100]
c) [67,100]

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.