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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 the four vowels do not come together?

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Important Questions on Permutations & Combinations

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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 different words can be formed with the letters of the word NAINITAL such that each of the word begin with L and end with T ?
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How many words can be made from the word MATHEMATICS in which vowels are together?
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How many words can be made from the word IMPORTANT in which both T do not come together?
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How many words can be made from the word TING TING TRING in which vowels occupy even positions?
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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?
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If all the letters of the word SEQUESTERED be arranged as in a dictionary, what is 50th  word?