0
How many distinguishable permutations of letters are possible in the word critics?
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.
Add your answer:
Earn +20 pts
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 permutations are there of the letters in the word effective?
The number of permutations of the letters EFFECTIVE is 9 factorial or 362,880. To determine the distinct permutations, you have to compensate for the three E's (divide by 4) and the two F's (divide by 2), giving you 45,360.
What is the number of distinguishable permutations of the letters in the word oregon?
360. There are 6 letters, so there are 6! (=720) different permutations of 6 letters. However, since the two 'o's are indistinguishable, it is necessary to divide the total number of permutations by the number of permutations of the letter 'o's - 2! = 2 Thus 6! ÷ 2! = 360
How many permutations are possible of the letters in the word Fresno?
There are 6! = 720 permutations.
What is the number of distinguishable permutations of the letters in the word EFFECTIVE?
The number of permutations of the letters EFFECTIVE is 9 factorial or 362,880. Since the letter E is repeated twice we need to divide that by 4, to get 90,720. Since the letter F is repeated once we need to divide that by 2, to get 45,360.
How many distinguishable permutations of letters are possible in the word class?
120?
How many distinguishable permutations of the letters CAT?
cat
How many distinguishable permutations of letters are in the word queue?
three
How many distinguishable permutations are there in the word letters?
7 factorial
How many distinguishable permutations are there for the word ALGEBRA?
There are 7 factorial, or 5,040 permutations of the letters of ALGEBRA. However, only 2,520 of them are distinguishable because of the duplicate A's.
What is the number of distinguishable permutations of the letters in the word GLASSES?
The solution is count the number of letters in the word and divide by the number of permutations of the repeated letters; 7!/3! = 840.
How may distinguishable permutations are possible with all the letters of the word ellises?
We can clearly observe that the word "ellises" has 7 letters and three pairs of letters are getting repeated that are 'e','l' and 's'. So, Number of distinguishable permutations = 7!/(2!2!2!) = 7 x 6 x 5 x 3 = 630.
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?
Normally, there would be 5!=120 different permutations* of five letters. Since two of the letters are the same, we can each of these permutations will be duplicated once (with the matching letters switched). So there are only half as many, or 60 permutations.* (the correct terminology is "permutation". "combination" means something else.)
Find the number of distinguishable permutations of letters in the word appliance?
The distinguishable permutations are the total permutations divided by the product of the factorial of the count of each letter. So: 9!/(2!*2!*1*1*1*1*1) = 362880/4 = 90,720
How many permutations are in the word October?
There are 7 factorial, or 5,040 permutations of the letters of OCTOBER. However, only 2,520 of them are distinguishable because of the duplicate O's.
How many distinguishable permutations are there of the letters in the word effective?
The number of permutations of the letters EFFECTIVE is 9 factorial or 362,880. To determine the distinct permutations, you have to compensate for the three E's (divide by 4) and the two F's (divide by 2), giving you 45,360.
