12. Using generating functions, find the number of solutions of the equation 41 type C(6,4).) (For ( 12. Using generating functions, find the number of solutions of the equation 41 type C(6,4).)...
Using generating functions, find the number of solutions of the equation (For ф type C(6,4), and for 5l type fact (5).) Using generating functions, find the number of solutions of the equation 7. (For φ type C(6,4).) Using generating functions, find the number of solutions of the equation (For φ type C(6,4).) Using generating functions, find the number of solutions of the equation (For ф type C(6,4), and for 5l type fact (5).) Using generating functions, find the number of...
10. Using generating functions, find the number of solutions of the equation 7. (For φ type C(6,4), and for 5! type fact (5).) 10. Using generating functions, find the number of solutions of the equation 7. (For φ type C(6,4), and for 5! type fact (5).)
11. Using generating functions, find the number of solutions of the equation 6, u1 +u2+... +u -22, where 1 < 6, i-1,...,4, 2 Suj ui (For (.) type C(6,4).) 11. Using generating functions, find the number of solutions of the equation 6, u1 +u2+... +u -22, where 1
11. Using generating functions, find the number of solutions of the equation 6, u1 +u2+... +u -19, where 1 < 7,i,...,4, 2 Suj ui 9. (For () type C(6,4).) 11. Using generating functions, find the number of solutions of the equation 6, u1 +u2+... +u -19, where 1
Using generating functions, find the number of solutions of the equation u1+u2+u3+u4+u5+u6=24 where 2 _< ui _<7, i=1,....,6
Using generating functions, find the number of solutions of the equation u1+u2+u3+u4+u5+u6=24 where 2 _< ui _<7, i=1,....,6
1. Using generating functions, find the number of ways to make change for a $100 bill using only dollar coins and $1, $2, and $5 bills. explain in detail
What generating functions can be used to find the number of ways in which postage of r cents can be pasted on an envelope using 1-cent, 3-cent, and 20-cent stamps? (a) Assume that the order the stamps are pasted on does not matter. (b) Assume that the stamps are pasted in a row and their order matters.
Find the number of solutions to x1 + x2 + x3 + x4 = 200 subject to xi E 220 (1 < i < 4) and x3, x4 < 50 in two ways: (i) by using the inclusion-exclusion principle, and (ii) using generating functions.
using the principle of inclusion-exclusion, find the number of solutions of the equation u1+u2+...+u6 = 15, where ui<6,i=1,..,6.