A life insurer issues a last-to-die joint life policy to a couple. One is rated as uninsurable and is estimated to die in less than five years with a variance of two years. The other insured person is rated standard, is assumed to outlive the uninsured person, and is expected to die with a variance of 10 years. Assume that the deaths are independent. (This is rarely true due to broken heart syndrome and joint risk.) What is the variance of the total number of years that this couple survives?

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.