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There are 5*4*3 = 60 permutations.
There are ten letters BUT there are 3 Ss and Ts and 2 Is. So the answer is 10!/(3!*3!*2!) = 50400
420.
This is a basic permutation problem. You have 6 elements, of which you need to select 3, without replacement, and order does matter (123 is different from 321). Permutations are covered by the wikipedia page on permutations. In short, however the answer is P(6, 3) = 6!/(6-3)! = 6*5*4 = 120.
240
The word "TENNESSEE" consists of 9 letters, with the following counts: T (1), E (4), N (2), and S (2). To calculate the number of distinct permutations, we use the formula for permutations of multiset: [ \frac{n!}{n_1! \times n_2! \times n_3! \times \ldots} ] This gives us: [ \frac{9!}{1! \times 4! \times 2! \times 2!} = \frac{362880}{1 \times 24 \times 2 \times 2} = \frac{362880}{96} = 3780. ] Thus, there are 3,780 distinct permutations of the letters in "TENNESSEE."
There are 5*4*3 = 60 permutations.
The word "TENNESSEE" consists of 9 letters, with the following frequency of each letter: T (1), E (4), N (2), S (2). To find the number of distinct permutations, we use the formula for permutations of a multiset: [ \frac{n!}{n_1! \times n_2! \times n_3! \times \ldots} ] This gives us: [ \frac{9!}{1! \times 4! \times 2! \times 2!} = \frac{362880}{1 \times 24 \times 2 \times 2} = \frac{362880}{96} = 3780 ] Thus, there are 3,780 distinct permutations of the letters in "TENNESSEE."
There are 8P5 = 8*7*6*5*4 = 6720
To find the number of five-letter words that can be formed using the letters a, a, g, m, and m, we can use the formula for permutations of multiset. The total permutations of the letters is given by ( \frac{5!}{2! \times 2!} = \frac{120}{4} = 30 ). Therefore, there are 30 distinct five-letter arrangements that can be formed with the given letters.
There are three that I can see, there's clip, board and lip.
9*8*7 / 2! / 3!
The only five letter word that can be made with those letters is 'ditto'.Other words that can be made with the letters in 'ditto' are:dodotIidittotot
There are ten letters BUT there are 3 Ss and Ts and 2 Is. So the answer is 10!/(3!*3!*2!) = 50400
A - Z means you can use the whole alphabet, which usually contains 26 letters. So a one-letter code would give you 26 permutations. 2 letters will give you 26 x 26 permutations. A three letter code, finally, will give you 26 x 26 x 26 , provided you don't have any restrictions given, like avoiding codes formed from 3 similar letters and such.
The word "DECAGON" has 7 letters, with the letter "A" appearing once, "C" appearing once, "D" appearing once, "E" appearing once, "G" appearing once, "N" appearing once, and "O" appearing once. To find the number of different 4-letter permutations, we need to consider combinations of these letters. Since all letters are unique, the number of 4-letter permutations is calculated using the formula for permutations of n distinct objects taken r at a time: ( P(n, r) = \frac{n!}{(n-r)!} ). Here, ( n = 7 ) and ( r = 4 ), so the number of permutations is ( P(7, 4) = \frac{7!}{(7-4)!} = \frac{7!}{3!} = 7 \times 6 \times 5 \times 4 = 840 ). Thus, there are 840 different 4-letter permutations that can be formed from the letters in "DECAGON."
The number of 7 letter permutations of the word ALGEBRA is the same as the number of permutation of 7 things taken 7 at a time, which is 5040. However, since the letter A is duplicated once, you have to divide by 2 in order to find out the number of distinct permutations, which is 2520.