# Combinatorics - math word problems

1. Coin and die
Flip a coin and then roll a six-sided die. How many possible combinations are there?
2. Area codes
How many 6 digit area codes are possible if the first number can't be zero?
3. Words
How many 3 letter "words" are possible using 14 letters of the alphabet? a) n - without repetition b) m - with repetition
4. Shelf
How many ways are there to arrange 6 books on a shelf?
5. Lock
A combination lock will open when the right choice of 3 numbers (from 1 to 16 inclusive) is selected. A. How many different lock combinations are possible? B. Is the combination lock named appropriately?
6. Commitee
A class consists of 6 males and 7 females. How many committees of 7 are possible if the committee must consist of 2 males and 5 females?
7. Kids
How many different ways can sit 8 boys and 3 girls in line, if girls want to sit on the edge?
8. Probabilities
If probabilities of A, B and A ∩ B are P (A) = 0.62 P (B) = 0.78 and P (A ∩ B) = 0.26 calculate the following probability (of union. intersect and opposite and its combinations):
9. Digits
Write the smallest and largest 1-digit number.
10. Vans
In how many ways can 9 shuttle vans line up at the airport?
11. Candy
How many ways can divide 10 identical candies to 5 children?
12. Monty Hall
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat.
13. Count of triangles
Given a square ABCD and on each side 8 internal points. Determine the number of triangles with vertices at these points.
14. 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?
15. Components
In the box are 8 white, 4 blue and 2 red components. What is the probability that we pull one white, one blue and one red component without returning?
16. Chocolates
In the market have 3 kinds of chocolates. How many ways can we buy 14 chocolates?
17. 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?
18. No. of divisors
How many different divisors have number ??
19. Scrap
From 6 products are 3 scrap. What is the probability that the random pick of 2 products have no defective product?
20. Toys
3 children pulled 12 different toys from a box. Many ways can be divided toys so that each children had at least one toy?

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

We will send a solution to your e-mail address. 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?