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How many distinguishable permutations of letters are possible in the word critics?
Wiki User
∙ 11y ago
The word critics has 7 letters which can be arranged in 7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 ways. To see this, imagine placing one of the 7 letters in the first slot. Then place a different letter in the second slot (there are only 6 letters left now), then 5 and so on down to 1. We multiply because we must do each of these steps to create a rearrangement of the word critics.
The problem then is that critics contains 2 'c's and 2 'i's, which are indistinguishable. For example, we might count "rtiicsc" several times by switching the places of the 'i's or the 'c's even though we cannot tell the difference in the word. So, we must divide out the repetition, by dividing by 2! = 2 * 1 twice. This corrects the over-counting from the duplicate letters.
So the correct result is 7!/(2! * 2!) = 1260 distinguishable permutations.
Wiki User
∙ 11y ago
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In how many ways can all the letters in the word mathematics be arranged in distinguishable permutations?
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In how many ways can all the letters in the word mathematics be arranged in distinguishable permutations?
The word mathematics has 11 letters; 2 are m, a, t. The number of distinguishable permutations is 11!/(2!2!2!) = 39916800/8 = 4989600.
How many distinguishable 5-letter combinations are possible of the letters of the word tight?
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Find the number of distinguishable permutations of letters in the word appliance?
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How many permutations are in the word October?
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How many distinguishable permutations are there of the letters in the word effective?
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