# Combinatorics - math word problems

1. Football league In the 5th football league is 10 teams. How many ways can be filled first, second and third place?
2. Candy How many ways can divide 10 identical candies to 5 children?
3. Playing cards How many possible ways are to shuffle 7 playing cards?
4. Pairs At the table sit 10 people, 5 on one side and 5 on the other side. Among them are 3 pairs. Every pair wants to sit opposite each other. How many ways can they sit?
5. Scrap From 6 products are 3 scrap. What is the probability that the random pick of 2 products have no defective product?
6. Sales From statistics of sales goods, item A buy 51% of people and item B buys 59% of people. What is the probability that from 10 people buy 2 item A and 8 item B?
7. Morse alphabet Calculate how many words of Morse code to create compiling commas and dots in the words of one to four characters.
8. Stacks Annie has a total of \$ 702. The money must be divided into stacks so that each buyer has the same amounth of dollars. How many options she have?
9. Coin and die Flip a coin and then roll a six-sided die. How many possible combinations are there?
10. Lock Combination lock will open when the right choice of 5 numbers (from 1 to 12 inclusive) is selected. A. How many different lock combinations are possible? B. Is he combination lock named appropriately?
11. Dices We will throw two dice. What is the probability that the ratio between numbers on first and second dice will be 1:2?
12. N-gon How many diagonals has convex 11-gon?
13. Event probability The probability of event P in 8 independent experiments is 0.33. What is the probability that the event P occurs in one experiment (probability is same)?
14. Subsets How many are all subsets of set ??
15. Balls From the urn in which are 7 white balls and 17 red, gradually drag 3-times without replacement. What is the probability that pulls balls are in order: red red red?
16. Shooter The probability that a good shooter hits the center of the target circle I is 0.1. The probability that the target hit intercircle is II 0.58. What is the probability that it hits the target circle I or II?
17. Pairs From the five girls and four boys teachers have to choose one pair of boy and girl. A) How many such pairs of (M + F)? B) How many pairs where only boys (M + M)? C) How many are all possible pairs?
18. Events Event P has probability of 0.84. What is the probability that the event P occurs in 3, 5, 7 try.
19. Pizza A school survey found that 12 out of 15 students like pizza. If 6 students are chosen at random, what is the probability that all 6 students like pizza?
20. Insurance The owner of the house is insured against natural disasters and pays 0.04% annually of the value of house 77 Eur. Calculate the value of the house. Calculate the probability of disaster, if you know that 48% of the insurance is to pay damages.

Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...

Would you like to compute count of combinations?