Permutations with repetition - practice problems - page 2 of 3

Directions: Solve each problem carefully. Show all your work.

Number of problems found: 47

Five-digit number repetition
How many five-digit numbers can we make from digits 2,3,4,6,7,9 if they can repeat with the digits?
Dice snake colors
Hansel has 4 identical yellow blocks and 3 identical blue blocks. How many different coloured sequences (snakes) can he make with them?
Comma dot characters
How many characters can we create from two commas and four dots?
Boy girl placement
Three boys and four girls. How many ways can they be placed side by side according to gender?
Element arrangement ways
Determine the number of arrangements of these six elements: a, a, a, b, b, c.
Dance couple arrangement
Six boys and six girls (among them Emil, Felix, Gertrude, and Hannah) want to dance. The number of ways they can make six (mixed) couples if Emil does not want to dance with Gertrude and Hannah wants to dance with Felix is?
Balls in row
Calculate the number of ways of placing four black balls, four turquoise balls, and five gold balls in a row.
How many 13
How many ways can X³ y⁴ z³ be written without an exponent?
Fruits
We want to plant five fruit trees in the garden, of which three are apple trees and two pears. How many different ways can we organize them?
Permutations with repetitions
How many ways can the digits 1, 2, 2, 3, 3, 3, 4 be permuted into four-digit, three-digit, and two-digit numbers without repetition? Example: 4 digits: 1223, 2213, 3122, 2313, 4321, etc. 3 digits: 122, 212, 213, 432, etc. 2 digits: 12, 21, 31, 23 Note: I
Syrups
In the shop, they sell three types of syrups - apple, raspberry, and orange. How many ways can you buy four bottles of syrup?
Seedbeds
The father wants to plant two seedbeds of carrots and two seedbeds of onion. Use a tree chart to find how many different options he has for placing the seedbeds.
Train wagon assembly
There are six tank cars, eight open and 12 closed wagons at the station. How many different trainsets can be assembled from them?
Wagons
We have six wagons: two white, two blue, and two red. We assemble trains from them; wagons of the same color are exactly the same, so if we change only two white wagons on a train, it's still the same train because I don't know any difference. How many di
Probability - cards
What is the probability that when dealing cards after 4, in the game Quartet (eight of fours), we will get the whole quartet?
STRESSED word
Each letter in STRESSED is printed on identical cards, one letter per card, and assembled in random order. Calculate the probability that the cards spell DESSERTS when assembled.
Three workplaces
How many ways can we divide nine workers into three workplaces if they need four workers in the first workplace, 3 in the second workplace, and 2 in the third?
Exercise Books Division Ways
How many ways can three children divide five small and six large exercise books? Admittedly, some get nothing.
Three-digit numbers
Use the number 4,5,8,9 to write all three-digit numbers without repetition. How many such numbers are there?
How many 2
How many three-lettered words can be formed from letters A B C D E G H if repeats are: a) not allowed b) allowed?

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