Aband is trying to determine how many songs to record for their new album. the band members want to record no more than 16 songs, and their album has to be shorter than 78 minutes. they can record short songs that are about 3 minutes in length or long songs that are about 5 minutes in length. which system of inequalities best represents the number of short songs (x) and the number of long songs (y) the band can record for the new album?

a) 3x+5y< 78
x+y≤16

b) 3x+5y< 16
x+y≤78

c) 3x+5y≤78
x+y< 16

d) 3x+5y≤16
x+y< 78

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.