Combinatorics | Number Theory Answers

Determine the number of ways to pick n fruits from k varieties of fruits where one picks at least l<k different fruits.

4. Jason is considering purchasing a new machine to make plastic silverware. The machine produces 1,000 pieces of silverware in two hours. One box contains 50 pieces of silverwares and sells for $3.00.

If the machine costs $9,000,and runs for many days, how many days will it take the machine to make enough silverware to pay for itself?

2009 2010
Lifter Distribution Lifter Distribution
Factory A 15% Factory A 20%
Factory B 15% Factory B 35%

If there are currently 45 heavy lifters at Factory A and the company increase it’s fleet by 60%, how many total lifters will be at factory A and Factory B after they are redistributed?

Hi my question is:

There are 12 UFC fights on. If I were to make one accumulated bet for all the 12 fights, how many accumulated bets must I make to bet on every single possible outcome. e.g. If I were to bet on all the favourites to win out of the 12 matches that would be one accumulated bet, if I were to bet on all the underdogs to win that would be 2 bets etc. etc.

how many bets must I make to win?

Model A Model B Model C Model D Model E
Time to manufacture 15 minutes 18 minutes 13 minutes 20 minutes 17 minutes
% Of monitors sold per total products 75% 73% 84% 95% 81%
Cost per monitor $175 $188 $145 $198 $170



A company manufactures computer monitors. Among the various models are top products, which bring high revenue.

Assuming the manufacturing lines are running for 9 hours a day for 7 days a week, which model brings in the highest revenue?

5. James is able to sell 15 of product A and 16 of the product B a week, Sally is able to sell 25 of product A and 10 of the product B a week, and Andrew is able to sell18 of the product A and 13 of the product B a week

If product A sells for $35.75 each and product B sells for $42.25 each, what is the difference in the amount of money earned between the most profitable and the least profitable seller?

How many 4 digit numbers are there where repetition of digits are allowed?

In the course of a given month, an RV dealer purchases 14 RVs from the manufacturer for $25,250 each and sells them at a 22% mark-up. The overall cost of doing business, ‘costs the RV dealer a totals of $45,000 each month in total.’

After these costs , how much profit does the RV dealer make a month?

Number of bijective functions from set A to itself when A contains 106 elements, is
a) 106
b) 106^2
c) 106!
d) 2^106

If n>=2, then number of surjections that can be defined from {1,2,3,...n} onto {1,2} is
a) 2n
b) nP2
c) 2^n
d) (2^n)-2