From the letters SASSAFRAS 2520 distinguishable permutations can be formed.
We have to find the total number of permutations for the word ‘SASSAFRAS’. Thus, we will apply the formula of finding permutations and calculate the factorial of the total number of letters in the word ‘SASSAFRAS’.
Further we will divide it by the factorial of the number of occurrences of each letter in this word.
Let the total permutations = 'p'
Total number of letters in the given word = 'n'
The formula of permutations for finding the total permutations is :
p = n!/(ma!.mb!.....mz!)
ma, mb,....., mz = number of occurrences of the letters a, b,.....,z in the given word.
The total number of letters in this word= 9
Thus, n = 9
Here, mS, mA, mF, and mR are the total number of occurrences of the letters S, A, F, and R respectively.
We see that mS = 4, mA = 3, mF = 1 and mR = 1,
Thus, we get number of permutations as
p = n! / (mS!.mA!.mF!.mR!)
p = 9!/(4!.3!.1!.1!)
We know that 9! = 362880, 4! = 24, 3! = 6 and 1! = 1.
By substituting these values, we get
p = 36288024.6.1.1
p = 362880144
Hence, p = 2520
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