Use generating functions to find the number of ways to distribute r jelly beans among eight children if  a) Each child gets at least one jelly bean b) Each child gets an even number of beans

Let A = {1,2,3,4,5} (a) How many subsets of A contain even numbers? (B) How many subsets of A contain an even number of elements?

Assume that the committee consists of 7 Trolls and 7 Ogres. A subcommittee consisting of 7 creatures is to be selected. (1) How many such subcommittees are possible if each subcommittee must contain exactly 4 Trolls and 3 Ogres?  (2) How many such subcommittees are possible if each subcommittee must contain at least 1 and no more than 3 Ogres?

According to the rules of NCAA volleyball, there must be exactly 6 players on the court at all times and each player has a unique designated position on the court. How many different starting position configurations are possible for the 6 starting players of an 8-member volleyball team that follows this rule?

A universal set U with 156 elements has been partitioned into three subsets, A, B, and C. If B is 5 times the size of A and C is 4 times the size of B, then how many elements are in B? (A) 7 (B) 30 (C) 36 (D) 120 (E) 156 (F) 5 (G) 31 (H) 6 OA OB D. O E OF H.