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- 1. Fill in the Blank
The five graduating classes in a school perform 1 dance each at the graduation ball. The class A perform the opening dance, a “palotás”. The order of the other dances is decided by a draw. How many different orders are possible?
- 2. Fill in the Blank
The lateral faces of a pyramid are painted in six different colours, and each face is painted in a single colour. How many different colourings are possible? (Two colourings are considered different if they cannot be obtained from each other by rotating the pyramid.)
- 3. Fill in the Blank
Four different kind of fruit trees are planted in a row: an apple tree, a pear tree, a peach tree and a plum tree. It is also given that there can be no peach tree at either end of the row. How many ways are there to plant these trees?
- 4. Fill in the Blank
Three digit numbers are formed using the digits 1, 2, 3, 4, 5 in such a way that non of them contains equal digits. How many numbers can be formed this way?
- 5. Fill in the Blank
How many 4-digit positive integers exist in the decimal system that have four different odd digits?
- 6. Fill in the Blank
How many (positive) three-digit odd numbers are there in the decimal system that consist of 3 different digits?
- 7. Fill in the Blank
How many four-digit numbers of four different digits can be made, such that each digit is an element of the set {1; 2; 3; 4; 5; 6; 7} ?
- 8. Fill in the Blank
How many seven-digit numbers divisible by four can be made out of digits of 1, 2, 3, 4, 5?
- 9. Fill in the Blank
How many six-digit numbers divisible by three are there that only contain digits of 1, 2, 3, 4, 5, such that each of these digits occurs at least once?
- 10. Fill in the Blank
In a test, students wrote three-letter codes made up of the letters A, B and C on their papers instead of their names. Every possible code from AAA to CCC was given to a student, and there were no students with the same code. How many students took the test?
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