A pharmaceutical company produces caffeine pills that are each supposed to contain 200 mg200\,\text{mg}200mg200, start text, m, g, end text of caffeine. A quality control expert took a random sample of pills from a batch and measured the amount of caffeine in each pill in the sample. They want to test if the mean amount is significantly different than 200 mg200\text{ mg}200 mg200, start text, space, m, g, end text.
H0​:μ=200 mg
Ha​:μ​ not equal 200 mg​

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.