10 Arabian horses are split into pairs to pull one of the distinct 4 carts in a race. If each cart is assigned to a pair, how many different assignments of horses to carts are possible? Choose the correct option
A) 420 B) 1260 C) 5220 D) 9450 E) 113400
# of ways 10 horses can be divided into 5 groups when order of the groups does not matter is: C210∗C28∗C26∗C24∗C225!=945C102∗C82∗C62∗C42∗C225!=945.   So we would have 945 different cases of dividing 10 horses into 5 groups:   1. A1A1, B1B1, C1C1, D1D1, E1E1 (each letter represent pair of horses);   2. A2A2, B2B2, C2C2, D2D2, E2E2;   ...   945. A945, B945, C945, D945, E945.   Now, we want to assign a pair (a letter in our case) to one of 4 distinct carts. For each case (out of 945) P45=120 would represent # of ways to choose 4 pairs out of 5 when order matters (as carts are distinct). OR C45 choose 4 different letters out of 5 and 4! - # of ways to assign 4 different letters to 4 distinct carts: C45∗4!=120C.   So total # of different assignments would be 945∗120=113400   Answer: 113400.
<result>E</result>
10 Arabian horses are split into pairs to pull one of the distinct 4 carts in a race. If each cart is assigned to a pair, how many different assignments of horses to carts are possible?