MATH 475 Midterm: MATH475 BOYLE-M SPRING2005 0101 MID SOL 2

• School: University of Maryland
• Department: Mathematics
• Course: MATH 475
• Professor: All

Document Summary

Exam 2 solutions math 475 spring 2005. The number of ways to choose (from 10 places) the 3 places for e, 2 places for 0, and so on, is the multinomial coe cient. Three of these six places must be chosen to place the remaining es. One proof: note that by the binomial theorem, the given sum is equal to [1+( 1)]99. Let ar denote the number of ways to get a sum r when 10 distinct dice are rolled. The generating function g(x) for the sequence (ar) is g(x) := = x10(1 + x + + x5)10 = x10(cid:16) 1 x6. Find a generating function for the number of ways to make r cents change in pennies, nickels and dimes. The generating function g(x) is (1 + x + x2 + x3 + )(1 + x5 + x10 + x15 + )(1 + x10 + x20 + x30 + )