The Bradys have a gross annual income of $175,000 and have been pre-approved for a 30-year mortgage loan at 3.375% as long as the back-end ratio does not exceed 36% The house they want to buy costs $360,000 and they plan to make a down payment of 20%. Their research shows that the semi-annual property taxes for this house are $3,450. They quote from their insurance company is for a $1,290 annual premium. The Bradys currently have a $579 monthly car payment and their monthly credit card bills average $2,100. Will the bank agree to finance the Bradys' dream home?

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.