A transposition takes the genes between indices i and j and places them between indices k and k + 1, for some i and j > i and k ∈/ {i, i + 1, . . . , j}. For example, for the chromosome h5, 9, 6, 2,...

A transposition takes the genes between indices i and j and places them between indices k and k + 1, for some i and j > i and k ∈/ {i, i + 1, . . . , j}. For example, for the chromosome h5, 9, 6, 2, 1, 4, 7, 3, 8i we could get the result h5, 1, 4, 7, 3, 9, 6, 2␣8i or h␣1, 4, 5, 9, 6, 2, 7, 3, 8i from a transposition. How many different transpositions are there for a 1000-gene chromosome?