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In how many ways can the letters of the word REPEAT be arranged?

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Important Questions on Permutations & Combinations

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In how many ways can the letters of the word TAMANNA be arranged?
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In how many ways can the letters of the word RECUPERATE be arranged?
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In how many ways can the letters of the word ASSASSINATION be arranged?
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In the above question (number 4) find the number of arrangements of four different letters of the word in a row?
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How many arrangements can be made out of the letters of the word COMMITTEE, taken all at a time, such that none of the four vowels come together?
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In how many ways can the letters of the word DUMDUMDIGADIGA be arranged?
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How many words can be made from the word MATHEMATICS in which vowels are together?
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If the different permutations of the word PRODIGIOUS are listed as in a dictionary, then what is the rank of the word PRODIGIOUS?