Variations - high school - practice problems
Number of problems found: 187
- Locker combination
Todd forgot the first two numbers of his locker combination. The numbers can be any number 1 through 6. What is the probability that he will guess the first number correctly and the second number incorrectly? - Five couples
In how many ways can 5 couples arrange themselves in a row if they stay together? - A basket 4
A basket contains 9 fruits, where 4 are oranges, and the rest are mangoes. Three fruits are taken out one at a time and put aside. Find the probability that 3 are oranges. - A ferry
A ferry with a capacity of 10 people takes a group of 13 men and 7 women across a river. Find the number of ways in which the group may be taken across the if all women go on the first group.
- Refrigerator 83310
How many possible ways can we store three lemonades, four mineral waters, and two juices in the refrigerator next to each other? - Married 83309
In how many ways can we seat five guests at a table, two of whom are married and want to sit next to each other? - Probability 82744
Ten books are placed randomly on one shelf. Find the probability that certain three books are placed next to each other. - Possibilities 82372
A hockey match played for three periods ended with a score of 2:3. How many possibilities are there on how the given thirds could have been completed? - Consecutively numbers
How many ways are there to arrange the numbers 3, 2, 15, 8, and 6 so that the even numbers are arranged in ascending order (not necessarily consecutively)?
- Different 79704
Thirty-two boys and 34 girls came to the dance. How many different dance pairs can they make, given that each team is given: they can only dance for 1 minute and then take turns in 5 seconds? Calculate how long the dance evening would last for all the pai - Four digit codes
Given the digits 0-7. If repetition is not allowed, how many four-digit codes that are greater than 2000 and divisible by 4 are possible? - Indistinguishable 74294
We have eight compartments where we put three indistinguishable balls and two distinguishable ones. How many options do we have? - Variations 70724
If we increase the number of elements by 2, the number of variations of the second class without repetition increases by 22. How many elements do we have initially? - Assemble 70414
How many ways can we assemble five wagons when sand is in three wagons and cement in two?
- Altogether 69994
Twelve players signed up for the squash tournament. Based on the lottery, they formed pairs, and in the first round, each pair played one match. The winners advanced to the second round, where they played each other one game at a time. How many matches we - Arrangements 68764
We have two identical blue balls and two identical red balls. We arrange them in a row in all ways. How many different arrangements are there? - Probability 68594
What is the probability that any two-digit number a) is divisible by five b) is it not divisible by five? - Competition 67314
The coach must choose two students from Sam, Jura, Emma, Dan, and Nika to go to the competition. He knows them well and knows that Samo will only go with Jura or Ema, and Dano will not go with Ema. How many pairs does the trainer have to choose from? - Different 66944
It was Tibor's birthday, and he bought 8 different cookies for his friends (Horalky, Tatanky, Kávenky, Attack, Mila, Anita, Mäta, Lina). He put them all in a box, and each friend could choose two pieces. Tanya chose first. Which two cookies could Táňa cho
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