120?
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
Just one - Mississippi. I checked the Scrabble dictionary and Webster's Second International dictionary (around 250,000 words in each).
165
Words that can be made with the letters in 'January' are:aajaranaurajarjayjurynarynayrayrayrunurnyarn
three
7 factorial
120?
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.
2520.
The word mathematics has 11 letters; 2 are m, a, t. The number of distinguishable permutations is 11!/(2!2!2!) = 39916800/8 = 4989600.
There are 7 factorial, or 5,040 permutations of the letters of OCTOBER. However, only 2,520 of them are distinguishable because of the duplicate O's.
10! permutations of the word "Arithmetic" may be made.
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 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 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.
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.