In collage there are 14 times as many students as professors. if together the students and professors number 37,500 how many students are there in the college?

3. a sum of $2700 is to be given in the form of 63 prizes. if the prize is of either $100 or $25, find the number of prizes of each type.

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.

Determine if each number is a whole number, integer, or rational number. include all sets to which each number belongs. 4. -12. 5. 7/8