A young equestrian loved to ride her horse all day long, dreaming of the day she would ride in the Kentucky Derby. One day in early April, she left home at

10:00 am and rode her stallion at a nice, steady 10 miles per hour away from

her house. At noon a call came in from the Derby saying she was in! Her

father immediately jumped on his scooter and rides at a breezy 15 miles per

hour to try and track her down and tell her the good news.

On what scale would you measure the number of minutes the father must

ride his scooter before catching up to his daughter?

O

A. Ten thousands

O

B. Thousands

O

c. Tens

O

D. Hundreds

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.