The number of ways to distribute 10 identical red pens and 14 identical blue pens among four persons such that each person gets 6 pens, is _____________.

Step-by-step solution

Let r_i and b_i be the number of red and blue pens given to the i -th person, where i = 1, 2, 3, 4 . Given that each person receives exactly 6 pens, we have: r_i + b_i = 6 b_i = 6 - r_i Since the number of blue pens must be non-negative ( b_i 0 ), we get r_i 6 . Also, r_i 0 . The total number of red pens is 10 , so: r₁ + r₂ + r₃ + r₄ = 10 The number of ways to distribute the pens is the number of non-negative integer solutions to this equation subject to 0 r_i 6 . This is equivalent to finding the coefficient of x¹