The diagram below models the layout at a carnival where g, r, p, c, b, and e are various locations on the grounds. grpc is a parallelogram.

parallelogram grpc with point b between c and p forming triangle gcb where gc equals 375 ft, cb equals 325 ft, and gb equals 425 ft, point e is outside parallelogram and segments be and pe form triangle bpe where bp equals 225 ft.

part a: identify a pair of similar triangles. (2 points)

part b: explain how you know the triangles from part a are similar. (4 points)

part c: find the distance from b to e and from p to e. show your work. (4 points)

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.