Let (P, ≤) be a finite poset. Define the numbers a₁,a₂,… (respectively, c₁,c₂,…) so that a₁ + … + a_k (respectively, c₁ + … + c_k) is the maximal number of elements of P which may be covered by k antichains (respectively, k chains.) Then the number e(P) of linear extensions of poset P is not less than ∏ a_i! and not more than n! / ∏ c_i!. A corollary: if P is partitioned onto disjoint antichains of sizes b₁,b₂,…, then e(P) ≥ ∏ b_i!.