Ms. Jimenez has 22 students in her class: 14 boys and 8 girls. She writes the name of each student on a slip of paper and puts each slip into a bag. Before Ms. Jimenez draws a name out of the bag, a student in the class makes the following claim: "Ms. Jimenez will probably draw a boy's name from the
bag because the ratio of boy names to girl names is 7:11."
The student made an incorrect claim. Which statement correctly describes the mistakes that were made?

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.