Two children want to walk together to visit their aunt, who lives exactly 8 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 15 blocks. How many different 15-block routes may they take to travel the shortest possible distance to their aunt’s house?
Choose the correct choice from the following choices.
A) 15!*8!*7!  B) 15!*8*7  C) 23!/(8!*7!)  D) 15!/(8!*7!)  E) 15/(8*7)
If they need to walk 8 blocks north and 7 blocks east, we can express this route as NNNNNNNNEEEEEEE. The question thus asks us how many ways we can arrange those letters.   The number of arrangements of 15 things is 15!   We then divide by the repetitions of N's and E's, which are 8! and 7! respectively.   The number of walking routes is 15!/(8!*7!).   The answer is 15!/(8!*7!).
<result>D</result>
Two children want to walk together to visit their aunt, who lives exactly 8 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 15 blocks. How many different 15-block routes may they take to travel the shortest possible distance to their aunt’s house?