Combinatorics - problemsWould you like to compute count of combinations?
- Phone numbers
How many 9-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated?
- Morse alphabet
Calculate how many words of Morse code to create compiling commas and dots in the words of one to five characters.
From statistics of sales goods, item A buy 54% of people and item B buys 58% of people. What is the probability that from 3 people buy 2 item A and 1 item B?
We will throw two dice. What is the probability that the ratio between numbers on first and second dice will be 1:2?
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?
The probability that the bulb can operate 4000 hours is 0.13. What is the probability that exactly one of eight bulbs can operate 4000 hours?
In the pool is numbers from 1 to 135. What is the probability that a randomly selected number is not a prime number?
In the box are 18 bulbs with power 60 W, 8 bulbs with power 40 W and 19 with 50 W. Calculate probability that a randomly selected bulb is:
- Football league
In the football league is 16 teams. How many different sequence of results may occur at the end of the competition?
What is the probability that a random word composed of chars T, I, O, D, I will be IDIOT?
- Football league
In the 2nd football league is 19 teams. How many ways can be filled first, second and third place?
Event J has probability of 0.17. What is the probability that the event J occurs in:
How many different ways can sit 5 boys and 5 girls in line, if girls want to sit on the edge?
- Seating rules
In a class are 22 seats but in 2.B class are only 14 students. How many ways can student seat? (The class has 11 benches. A bench is for a pair of students.) Result (large number) logarithm and thus write down as powers of 10.
- The dice
What is the probability of events that if we throw a dice is rolled less than 6?
How many different combinations of two-digit number divisible by 4 arises from the digits 3, 5 and 7?
- 7 heroes
5 heroes galloping on 5 horses behind. How many ways can sort them behind?
- 2nd class variations
From how many elements you can create 6480 variations of the second class?
- Two doctors
Doctor A will determine the correct diagnosis with a probability 80% and doctor B with a probability 72%. Calculate probability of correct diagnosis if patient is diagnosed by both doctors.
- Playing cards
How many possible ways are to shuffle 7 playing cards?