Permutations with repetition - practice problems - last page

Direction: Solve each problem carefully and show your solution in each item.

Number of problems found: 28

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?
Positive integer integral
How many different sets of a positive integer in the form (x, y, z) satisfy the equation xyz=1400?
Kenneth 2
Kenneth has 100 pennies, 20 nickels, 10 dimes, and 4 quarters. How many ways can he choose coins that total 25 cents?
Word OPTICAL
Find the number of possible different arrangements of the letters of the word OPTICAL such that the vowels would always be together.
Permutations with repetitions
How many times can the input of 1.2.2.3.3.3.4 be permutated into four digits, three digits, and two digits without repetition? Ex: 4 digits = 1223, 2213, 3122, 2313, 4321. . etc 3 digits = 122.212.213.432. . etc 2 digits = 12, 21, 31, 23 I have tried the
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
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.
Salami
We have six kinds of salami that have ten pieces and one kind of salami that has four pieces. How many ways can we distinctly choose five pieces of salami?

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