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How many permutations can you get out of an eight word phrase?There are 8! = 40320 permutations. How many permutations are possible of the letters in the word Fresno?There are 6! = 720 permutations. How many permutations are in the word swimming?2 How many permutations are there of the letters in the word greet?tt How many permutations are in the word united?UNITED = 6 letters The letters in the word UNITED did not repeat so the number of permutations = 6! = 6x5x4x3x2 =720 #(10!)/(2!2!3!) = 151200# There are a total of #10# letters. If they were all distinguishable then the number of distinct arrangements would be #10!#. We can make them distinguishable by adding subscripts:
If we remove the subscripts from the letter #O#'s, then it no longer makes any difference what order the #O#'s are in and we find that #1/(2!) = 1/2# of our #10!# arrangements are identical to the other half. So there are #(10!)/(2!)# possible arrangements of the letters:
If we remove the subscripts from the letter #K#'s a similar thing happens and we are left with half again. So there are #(10!)/(2!2!)# possible arrangements of the letters:
Finally, since #E_1#, #E_2# and #E_3# can be arranged in #3!# possible orders, then when we remove the subscripts from the #E#'s there are #(10!)/(2!2!3!)# distinct arrangements of the letters:
#(10!)/(2!2!3!) = (10!)/(2*2*6) = (10!)/(4!) = 10 * 9 * 8 * 7 * 6 * 5 = 151200# Number of letters in the word BOOKKEEPING = 11. There are three doubles and 5 singles. We can take 3 cases to use 5 letters. Case-1 Taking 2 doubles and 1 other. Number of permutaions formed by 2doubles and 1 other
Case-2 Taking 1 double and 3 others. Number of permutaions formed by 1double and 3 others
Case-3 Taking 5 others. Number of permutaions formed by 5 distinct letters
Total number of perputations formed by using 5 letters of the word BOOKKEEPING is 540 + 6300 + 6720 = 13560. How many ways can you scramble the letters in bookkeeper?There are (53)=10 ways to do this, of which just one is in alphabetical order.
How many permutations are there of the letters?To calculate the amount of permutations of a word, this is as simple as evaluating n! , where n is the amount of letters. A 6-letter word has 6! =6⋅5⋅4⋅3⋅2⋅1=720 different permutations.
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