  Young tableaux are ubiquitous in various branches of mathematics. There are
two counting formulas for standard Young tableaux. The first involves a
determinant and goes back to Frobenius and Young, and the second is the hook
formula by Frame, Robinson and Thrall. We present a generalization of the
determinant formula for semistandard Young tableaux of given shape and of given
content. Our counting formula -- though not a determinant -- is a
generalization of the determinant formula by Frobenius and Young.
