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It is 6! = 6*5*4*3*2*1 = 720

Q: Find the number of distinguishable permutations of the letters honest?

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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.

No, sometimes they will be equal (when all items being permutated are all different, eg all permutations of {1, 2, 3} are distinguishable).

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 1I 1P 60 2T 1A 1M 1U 1S 1Multiply these numbers together. 1 x1 x6 x2 x1 x1 x1 x1 x1 = 12Divide 12! by this number. 479001600 / 12 = 39,916,800 Distinguishable Permutations.

Since there are no duplicate letters in the word RAINBOW, the number of permutations of those letters is simply the number of permutations of 7 things taken 7 at a time, i.e. 7 factorial, which is 5040.

The number of permutations of the letters in PREALGEBRA is the same as the number of permutations of 10 things taken 10 at a time, which is 3,628,800. However, since the letters R, E, and A, are repeated, R=2, E=2, A=2, you must divide that by 2, and 2, and 2 (for a product of 8) to determine the number of distinctpermutations, which is 453,600.

Related questions

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.

The word mathematics has 11 letters; 2 are m, a, t. The number of distinguishable permutations is 11!/(2!2!2!) = 39916800/8 = 4989600.

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

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

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.

Take the total number of letters factorial, then divide by the multiple letters factorial (a and e). 7! / (2!*2!) or 1260.

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.

2520.

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.

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.

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

September has 9 letter, of which one appears 3 times. So the number of distinct permutations is 9!/3! = 120,960