Question: Given S = {1, 2, . . . , n}. How many unordered pairs {A, B} are there where A, B are nonempty subsets of

Given S = {1, 2, . . . , n}. How many unordered pairs {A, B} are there where A, B are nonempty subsets of S with A B = .

Consider the word OHMYGODIMONFIRE. How many distinguishable ways are there to rearrange the letters?

How many sequences of 1s and 1s of length 10 are there that sum up to 2?

How many 4-letter words can be obtained using any of the 26 letters of the alphabet, if repetition of letters is allowed?

How many 4-letter words can be obtained using any of the 26 letters of the alphabet, if repetition is not allowed?

How many 4-letter words contain at least one repeated letter? How many 4-letter words contain the letter X?

How many 4-letter words consist of only the letters X and/or Y? (The words XXXX and YYYY are included in this count.)

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