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The number of permutations of n distinct objects is n! = 1*2*3* ... *n.
If a set contains n objects, but k of them are identical (non-distinguishable), then the number of distinct permutations is n!/k!.
If the n objects contains j of them of one type, k of another, then there are n!/(j!*k!).
The above pattern can be extended. For example, to calculate the number of distinct permutations of the letters of "statistics":
Total number of letters: 10
Number of s: 3
Number of t: 3
Number of i: 2
So the answer is 10!/(3!*3!*2!) = 50400
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What is the number of distinguishable permutations?
The formula for finding the number of distinguishable permutations is: N! -------------------- (n1!)(n2!)...(nk!) where N is the amount of objects, k of which are unique.
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
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.
What is the number of distinguishable permutations?
The formula for finding the number of distinguishable permutations is: N! -------------------- (n1!)(n2!)...(nk!) where N is the amount of objects, k of which are unique.
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 are number of distinguishable permutations in the word Georgia?
2520.
How many distinguishable permutations of the letters CAT?
cat
How many distinguishable permutations can be made out of the word cat?
act
How many distinguishable permutations are there in the word letters?
7 factorial
How many distinguishable permutations of letters are in the word queue?
three
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 distinguishable permutations of letters are possible in the word class?
120?
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 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.
What are different counting techniques?
What are the different counting techniques
