Factorial - examples
- Cancel fractions
Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)!
In how many ways can 5 shuttle vans line up at the airport?
How many ways can 7 people sit on 2 numbered chairs (eg seat reservation on the train)?
How many ways can 8 guests sit down on 10 seats standing in a row?
What is the probability that a random word composed of chars H, T, M, A will be MATH?
How many ways are there to arrange 6 books on a shelf?
- Playing cards
How many possible ways are to shuffle 6 playing cards?
At the table sit 8 people, 4 on one side and 4 on the other side. Among them are 3 pairs. Every pair wants to sit opposite each other. How many ways can they sit?
How many ways can divide 16 identical candies to 4 children?
How many different ways can sit 8 boys and 3 girls in line, if girls want to sit on the edge?
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?
- School trip
Class has 17 students. What different ways students can be accommodated in the hostel, where available 3× 2-bed, 1× 3-bed and 2× 4-bed rooms. (Each room has its own unique number)
- Hockey players
After we cycle five hockey players sit down. What is the probability that the two best scorers of this crew will sit next to each other?
How many different 7 digit natural numbers in which no digit is repeated, can be composed from digits 0,1,2,3,4,5,6?
On each side of the square is marked 10 different points outside the vertices of the square. How many triangles can be constructed from this set of points, where each vertex of the triangle lie on the other side of the square?
In elections candidate 10 political parties. Calculate how many possible ways can the elections finish, if any two parties will not get the same number of votes.
- Friends in cinema
5 friends went to the cinema. How many possible ways can sit in a row, if one of them wants to sit in the middle and the remaining's place does not matter?
- Math logic
There are 20 children in the group, each two children have a different name. Alena and John are among them. How many ways can we choose 8 children to be among the selected A) was John B) was John and Alena C) at least one was Alena, John D) maximum one w
Determine how many ways can be chosen two representatives from 34 students to school tournament.
- Seating rules
In a class are 24 seats but in 7.B class are only 18 students. How many ways can student seat? (The class has 12 benches. A bench is for a pair of students.) Result (large number) logarithm and thus write down as powers of 10.