Two children want to walk together to visit their aunt, who lives exactly 9 blocks north and 7 blocks east of their current location. If they travel only along streets and do not travel diagonally, the shortest possible route connecting the two points is exactly 16 blocks. How many different 16-block routes may they take to travel the shortest possible distance to their aunt’s house?
Choose the correct answer:
A) 9!*7!
B) 16*9*7
C) 16!*9!*7!
D) 16!/(9*7)
E) 16!/(9!*7!)
If they need to walk 9 blocks north and 7 blocks east, we can express this route as NNNNNNNNNEEEEEEE. The question thus asks us how many ways we can arrange those letters.   The number of arrangements of 16 things is 16!   We then divide by the repetitions of N's and E's, which are 9! and 7! respectively.   The number of walking routes is 16!/(9!*7!).   The answer is 16!/(9!*7!).
<result>E</result>
Two children want to walk together to visit their aunt, who lives exactly 9 blocks north and 7 blocks east of their current location. If they travel only along streets and do not travel diagonally, the shortest possible route connecting the two points is exactly 16 blocks. How many different 16-block routes may they take to travel the shortest possible distance to their aunt’s house?