Question

9. Suppose 100 identical tickets for rides are distributed among 40 children at a carnival. (a) How many ways can the tickets be distributed, if each child receives at least two tickets, and all the tickets are distributed? (b) How many ways can the tickets be distributed, if each child receives at least one ticket, and some tickets may be left over? (c) Suppose one child has twelve tickets, and each ticket may be used on any of six different rides. How many ways can the child spend her tickets, if she can choose any ride any number of times, and the order of choice is unimportant?

Answer 1

Suppoae 100 identical tickets for rides are distributed among 40 children at a carnival.

suppose 100 identical tickets for rides are distributed among 40 children at a carnival. (a) How many ways can the ticket be distributed, if each child receives at least two tickets, and all the tickets are distributed ? (b) How many ways can the tickets be distributed, if each child receives at least one ticket, and some tickets may be left over? (C) suppose one child has twelve tickets, and each ticket may be used on any of six different rides. How many ways can the child spend her tickets, if she can choose any ride any number of times, and the order of choices is unimportent?

Answer: (a) one each child has received their two tickets are 20. I dentical tickets left to be given out to the 40 children with no restruction is 40+ 20-'c - 59,0 -2.494563003€ +15 ways. (b) there are to identical tickets left to be given out to the 40 children 20 41760-1660 100.60 = 1.3746 23414E + 28 ways. (C) This is some as the noi of ways of solving at a tag tay tagtag = 12 6+12-14 12 = 17612 26188 ways.