Combinatorics

Question

Consider a sequence of 10 A's and 8 B's placed in a Row. By a run we mean one or more letters of the same type placed side by side. Here is a arrangement of 10 A's and 8 B's which contains 4 runs of A and 4 runs of B:
AAA  BB  A  BBB  AA   B   AAAA   BB
In how many ways can 10 A's and 8 B's be arranged in a row so that there are 4 runs of A and 4 runs of B.
a) 2*(9c3)(7c3)  
b) (9c3)(7c3)
c) (10c4)(8c4)
d) (10c5)(8c5)
 

Answer 1

C) (10c4)(8c4)