Word Rearrangements: all problems

Focus mode: every practice problem from the chapter, one after another.

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Problem 3.3.1

How many ways are there to arrange the letters of the word MATH?

Problem 3.3.2

How many ways are there to arrange the letters of the word MISSISSIPPI?

Problem 3.3.3

Find the number of ways to order the letters in PINEAPPLE.

Problem 3.3.4

How many ways are there to misspell the word MISSPELLED?

Problem 3.3.5

How many arrangements of the word BOTTLE are there such that the 2 T's and O remain together?

Problem 3.3.6

AMC 10

A child builds towers using identically shaped cubes of different color. How many different towers with a height 8 cubes can the child build with 2 red cubes, 3 blue cubes, and 4 green cubes? (One cube will be left out.)

Problem 3.3.7(additional)

You have 6 apples, 3 pears, and 2 oranges. Assuming the same type of fruits are indistinguishable, how many distinct ways are there to place the fruits in a line if the 2 oranges must be next to each other?

Problem 3.3.8(additional)

AMC 10

How many distinguishable arrangements are there of 1 brown tile, 1 purple tile, 2 green tiles, and 3 yellow tiles in a row from left to right? (Tiles of the same color are indistinguishable.)

Problem 3.3.9

MATHCOUNTS

How many distinct four-letter permutations are possible using four of the ten letters in MATHCOUNTS?

Problem 3.3.10

AMC 8

In how many ways can the letters in BEEKEEPER be rearranged so that two or more Es do not appear together?

Problem 3.3.11

AHSME

How many distinguishable rearrangements of the letters in $CONTEST$ have both the vowels first? (For instance, $OETCNST$ is one such arrangement but $OTETSNC$ is not.)

Problem 3.3.12

Omega Learn

If the letters of the word SMILE are rearranged in all possible ways, and arranged in alphabetical order like in a dictionary, then what will be the rank of the word SLIME?