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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
What else can I help you with?
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
What is distinguishable permutation?
Distinguishable permutations refer to the arrangements of a set of objects where some objects may be identical. In contrast to regular permutations, which count all arrangements as unique, distinguishable permutations account for identical items by dividing the total permutations by the factorial of the counts of each identical item. This calculation ensures that arrangements that are the same due to identical items are not overcounted. For example, in the word "BANANA," the distinguishable permutations would be calculated to avoid counting the identical "A"s and "N"s multiple times.
How many distinguishable permutations can be made out of the word cat?
act
How many distinguishable permutations of letters are in the word queue?
three
How many distinguishable permutations are there in the word letters?
7 factorial
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?
How many distinguishable and indistinguishable permutations are there in the word algrebra?
The word "algrebra" has 8 letters, with the letter 'a' appearing twice and 'r' appearing twice. To find the number of distinguishable permutations, we use the formula for permutations of multiset: ( \frac{n!}{n_1! \times n_2!} ), where ( n ) is the total number of letters and ( n_1, n_2 ) are the frequencies of the repeating letters. Thus, the number of distinguishable permutations is ( \frac{8!}{2! \times 2!} = 10080 ). Since all letters are counted in this formula, there are no indistinguishable permutations in this context.
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.
