While in Canada you get sick and go to the emergency room of a local hospital. The doctor there diagnoses your illness and prescribes a dose of medicine that will cure you completely. The order is for 50 mg of the medicine. A nurse comes in with a liquid and you ask to see the bottle. The bottle says 100 mg of medicine per 15 ml of liquid. How many milliliters should the nurse give you?

Would she need to bring that to you in a little cup, a glass, or a large bottle?

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.