Question

(5 p) Two ants move along a rectangular mesh at a pace of 1 block per timeslice. The two ants start towards each other simultaneously, one from the origin, and the other from (12, 14). They bump into each other after 13 timeslices, earliest possible, at (7, 6). In how many different ways can that happen? 3. (Bump in Manhattan, X blocks East, Y blocks North) (5 p) 5. One shuffles at random the letters in RAZZMATAZZ. Find the probability that the new word also containts (5 p) (5 p) two non-adjacent pairs of 'ZZ':s, e.g., ZZAZZTARAM or MZZARAZZTA (but not AZZZZTARAM)?

Answer 1

3)

number of ways move from one corner to other in m*n grid is (m+n)Cn

For Ant 1 (0,0) to (7,6) , m = 7 , n = 6

hence number of ways = (7+6)C6 = 13C6

For Ant B , (12,14) to (7,6) , m = 5, n = 8

number of ways = (5 +8)C8 = 13C8

hence answer is 13C6 * 13C8