Permutations - practice problems

Number of problems found: 183

Socks
Ben's favorite colors are blue and green. He has six blue socks and six green socks in his sock drawer. Unfortunately, they are completely mixed up, and one day, he has to grab some socks to wear in complete darkness. How many socks (minimum) does he have
Non equivalent ints
Two n-digit integers are said to be equivalent if one is a permutation of the other. Find the number of 5-digit integers such no two is equivalent. If the digit 5,7,9 can appear at most one, how many non-equivalent five-digit integers are there?
A fair coin
A fair coin is tossed twice. Write down the set of possible outcomes. What is the probability of obtaining it? I. Exactly one head ii. No head
Equilateral 75284
Given are 6 line segments with lengths of 3 cm, 4 cm, 5 cm, 7 cm, 8 cm, and 9 cm. How many equilateral triangles can make from them? List all the options.
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?
Seven segments display
Electronic devices sometimes make use of the type of digits below, where each digit uses a number of short stripes. For example, seven uses three small stripes. What is the largest three-digit number that you can make if you use twenty stripes?
Parking 72644
How many ways can ten cars park side by side in a parking lot?
Numbers 72404
How many numbers are less than 200, the digits sum of which is 6?
Probability 72324
We used the digits 2, 3, 4, 5, and 7 when entering the PIN code, and we only used each digit once. What is the probability that someone will guess our PIN code on the first try?
Three-digit 72184
How many three-digit numbers can be created from the numbers 1, 2, 3, and 4 if you can repeat them?
Identical 71234
How many ways can you divide two identical apples and: a) 3, b) 4, c) 5 identical pears between Janka and Mařenka?
Assemble 70414
How many ways can we assemble five wagons when sand is in three wagons and cement in two?
Classical 69634
Peter, Jano, Alice, and Rebecca went to a classical music concert. How many different ways can they sit in the four free seats if Rebecca wants to sit with John?
Michalovci 69494
How many different courses could the match between AC Michalovci and Juvent Turiec have, which ended 2: 1?
Competition 69474
There are ten girls and seven boys in the dance group. Only one mixed couple is to go to the competition. How many are all possible pairs from which we can choose a pair for the competition?
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?
Constructed 67424
There are six lines 3 cm, 4 cm, 5 cm, 7 cm, 8 cm, and 9 cm long, two of each length. How many isosceles triangles can be constructed from them? List all options.
Gradually 67284
Petra borrowed four books from the library at the beginning of the summer holidays. How many orders in which she could gradually read them?

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