# Combinatorics - math word problems

1. A student
A student is to answer 8 out of 10 questions on the exam. a) find the number n of ways the student can choose 8 out of 10 questions b) find n if the student must answer the first three questions c) How many if he must answer at least 4 of the first 5 qu
2. Families 2
There are 729 families having 6 children each. The probability of a girl is 1/3 and the probability of a boy is 2/3. Find the the number of families having 2 girls and 4 boys.
3. Combinations 7
A multi-course meal has 3 choices. 3 appetizers, 4 main courses, and 3 desserts. How many different combinations to choose from?
4. How many 2
How many three lettered words can be formed from letters A B C D E G H if repeats are: a) not allowed b) allowed
5. Left handed
It is known that 25% of the population is left-handed. What is the probability that there is a maximum of three left-handers at a seminar where there are 30 participants?
6. Prime number
Jan wrote any number from 1 to 20. What is the probability that he wrote the prime number?
7. Component fail
There is a 90 percent chance that a particular type of component will perform adequately under high temperature conditions. If the device involved has four such components, determine the probability that the device is inoperable because exactly one of the
8. Boys and girls
There are eight boys and nine girls in the class. There were six children on the trip from this class. What is the probability that left a) only boys b) just two boys
9. Inverted nine
In the hotel,, Inverted nine" each hotel room number is divisible by 6. How many rooms we can count with three-digit number registered by digits 1,8,7,4,9?
10. PIN code
PIN on Michael credit card is a four-digit number. Michael told this to his friend: • It is a prime number - that is, a number greater than 1, which is only divisible by number one and by itself. • The first digit is larger than the second. • The second
11. Mumbai
A job placement agency in Mumbai had to send ten students to five companies two to each. Two of the companies are in Mumbai and others are outside. Two of the students prefer to work in Mumbai while three prefer to work outside. In how many ways assignmen
12. To improve
To improve her handwriting Paula practices writing the numbers 1 to 200 in words. How many times will she have written the word "one" in all?
13. A book
A book contains 524 pages. If it is known that a person will select any one page between the pages numbered 125 and 384, find the probability of choosing the page numbered 252 or 253.
14. Peaches
There are 20 peaches in the pocket. 3 peaches are rotten. What is the probability that one of the randomly picked two peaches will be just one rotten?
15. Dinning room
How many different combinations can we choose if there are 3 soups, 5 kinds of main dish and 2 desserts in the dining room?
16. Sweater
Dana confuses sweater and wool has a choice of seven colors. In how many ways she can choose from three colors to the sleeves?
17. Digit sum
How many are three-digit numbers that have a digit sum of 6?
18. Lunch
Seven classmates go every day for lunch. If they always come to the front in a different order, will be enough school year to take of all the possibilities?
19. The big clock
The big clock hands stopped at a random moment. What is the probability that: a) a small hand showed the time between 1:00 and 3:00? b) the big hand was in the same area as a small hand in the role of a)? c) did the hours just show the time between 21:00
20. Utopia Island
A probability of disease A on the island of Utopia is 40%. A probability of occurrence among the men of this island, which make up 60% of all the population (the rest are women), is 50%. What is the probability of occurrence of A disease among women on Ut

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