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Find the number of distinguishable permutations of the letters in the word hippopotamus?
First of all, find the total number of not-necessarily distinguishable permutations. There are 12 letters in hippopotamus, so use 12! (12 factorial), which is equal to 12 x 11x 10 x9 x8 x7 x6 x5 x4 x3 x2 x1. 12! = 479001600.
Then count the of each letter and calculate how many permutations of each letter can be made. For example, here is 1 h, so there is 1 permutation of 1 h.
H 1
I 1
P 6
0 2
T 1
A 1
M 1
U 1
S 1
Multiply these numbers together. 1 x1 x6 x2 x1 x1 x1 x1 x1 = 12
Divide 12! by this number. 479001600 / 12 = 39,916,800 Distinguishable Permutations.
What else can I help you with?
How many distinguishable permutations are there of the letters of the word rectangle?
The word "rectangle" consists of 9 letters, with the letter 'e' appearing twice and all other letters being unique. To find the number of distinguishable permutations, we use the formula for permutations of a multiset: (\frac{n!}{n_1! \cdot n_2! \cdots n_k!}), where (n) is the total number of letters and (n_i) are the frequencies of the distinct letters. Thus, the number of distinguishable permutations is (\frac{9!}{2!} = \frac{362880}{2} = 181440).
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.
Find the number of distinguishable permutations of the letters honest?
It is 6! = 6*5*4*3*2*1 = 720
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.
How many permutations of the letters a through J are there?
The letters from a to J consist of 10 distinct letters. The number of permutations of these letters is calculated using the factorial of the number of letters, which is 10!. Therefore, the total number of permutations is 10! = 3,628,800.
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 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.
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
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 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.
Find the number of distinguishable permutations of the letters honest?
It is 6! = 6*5*4*3*2*1 = 720
Find the number of distinguishable permutations of the letters in the word manatee?
Take the total number of letters factorial, then divide by the multiple letters factorial (a and e). 7! / (2!*2!) or 1260.
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.
What are number of distinguishable permutations in the word Georgia?
2520.
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.
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.
