Two children want to walk together to visit their aunt, who lives exactly 7 blocks north and 6 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 13 blocks. How many different 13-block routes may they take to travel the shortest possible distance to their aunt’s house? Pick:
A) 13
B) (13!)/(7!6!)
C) (20!)/(13!7!)
D) 7!6!
E) 13!7!6!
If they need to walk 7 blocks north and 6 blocks east, we can express this route as NNNNNNNEEEEEE. The question thus asks us how many ways we can arrange those letters.   The number of arrangements of 13 things is 13!   We then divide by the repetitions of N's and E's, which are 7! and 6! respectively.   The number of walking routes is 13!/(7!6!).   The answer is (13!)/(7!6!).
<result>B</result>
Two children want to walk together to visit their aunt, who lives exactly 7 blocks north and 6 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 13 blocks. How many different 13-block routes may they take to travel the shortest possible distance to their aunt’s house?