# Combinatorics - math word problems

1. Two aces
From a 32 card box we randomly pick 1 card and then 2 more cards. What is the probability that last two drawn cards are aces?
2. In the orchard
In the orchard, they planted 25 apple trees, 20 pears, 15 plums and 40 marbles. A strong late frost, however, destroyed a fifth of all new trees. Unfortunately, it was all the trees of one kind of fruit. What is the probability that the plums have died ou
3. Salami
How many ways can we choose 5 pcs of salami if we have 6 types of salami for 10 pieces and one type for 4 pieces?
4. Elements
If the number of elements is decreased by two the number of permutations is decreased 30 times. How many elements are?
5. Seagull
Artificially created island in the shape of a circle with a radius of 50 m is overgrown with grass. The only exception is a landing area for helicopters in the shape of a rectangle measuring 15 m and 8 m. What is the probability that the flying seagull (w
6. Combinations
How many elements can form six times more combinations fourth class than combination of the second class?
7. Points in plane
The plane is given 12 points, 5 of which is located on a straight line. How many different lines could by draw from this points?
8. Combinations
If the number of elements increase by 3, it increases the number of combinations of the second class of these elements 5 times. How many are the elements?
9. Variation equation
Solve combinatorics equation: V(2, x+8)=72
10. First man
What is the likelihood of a random event where are five men and seven women first will leave the man?
11. Four swords
Obelix has three helmets, four swords and five shields. How many swords must make at the blacksmith forge Metallurgix to be able to walk another 90 days in unique armor?
12. Distribution function
X 2 3 4 P 0.35 0.35 0.3 The data in this table do I calculate the distribution function F(x) and then probability p(2.5
13. Tokens
In the non-transparent bags are red, white, yellow, blue tokens. We 3times pull one tokens and again returned it, write down all possibilities.
14. Ice cream
Annie likes much ice cream. In the shop are six kinds of ice cream. In how many ways she can buy ice cream to three scoop if each have a different flavor mound and the order of scoops doesn't matter?
15. Competition
15 boys and 10 girls are in the class. On school competition of them is selected 6-member team composed of 4 boys and 2 girls. How many ways can we select students?
16. Normal Distribution
At one college, GPA's are normally distributed with a mean of 3.1 and a standard deviation of 0.4. What percentage of students at the college have a GPA between 2.7 and 3.5?
17. Cards
The player gets 8 cards of 32. What is the probability that it gets a) all 4 aces b) at least 1 ace
18. Metals
In the Hockey World Cup play eight teams, determine how many ways can they win gold, silver and bronze medals.
19. Prize
How many ways can be rewarded 9 participants with the first, second and third prize in a sports competition?
20. Permutations without repetition
From how many elements we can create 720 permutations without repetition?

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