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Use generating functions to determine the number of different ways 15 identical donuts can be given to five students if each student receives at least three but no more than 7 donuts.(Show all the steps) Click here if the table not showing TABLE 1 Useful Generating Functions. G(x) ak n (1 + x)" C(n, k)x* C(n, k) k=0 = 1+ C(n,1)x+ C(n, 2)x2 tr" 71 (1 + ax)" = C(n, k) C(n, k)a* xk C(n, k)ak k=0 = 1+ C(n, 1)ax + C(n, 2)ax2 + ... + a"x" n (1 + x)" C(n,k/r) ifr | k; 0 otherwise C(n, k) C(n,k)x"* k=0 =1+ C(n. 1)x' + C(n, 2)x2r + ... + x 1- xn+1 - * = 1 + x + x2 +...+x" 1 if k