The correct option is B 1008
Prime factorization of (7!)3=(24×32×5×7)3=212×36×53×73
Now, for a multiple of 10, there should be at least one 5 and at least one 2 present in the number.
Therefore, the number can be like =21−12×30−6×51−3×70−3
Hence, number of factors =12×7×3×4=1008