# 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?

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