Let S be a multiset with k elements whose repetition numbers are n,...,nk. Prove that if...

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Let S be a multiset with k elements whose repetition numbers are n₁,...,nk. Prove that if r ≤ n₁ + ··· +nk, the number of r- combinations of elements in S is the coefficient of " in the polynomial expansion of II₁ / ₁ (¹ + x + ... + x¹₁ П Let S be a multiset with k elements whose repetition numbers are n₁,...,nk. Prove that if r ≤ n₁ + ··· +nk, the number of r- combinations of elements in S is the coefficient of " in the polynomial expansion of II₁ / ₁ (¹ + x + ... + x¹₁ П

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