Question

How many distinguishable permutations can be formed from the letters in the word sassafras

Answer 1

In the word "SASSAFRAS", there 2520 permutations can be formed.

Permutation :

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.

The order of arrangement in permutation is in linear form.

In the given word is “SASSAFRAS”. There are total 9 letters in which some letters appears several times, that is

 S = 4 times.

 A = 3 times.

 F = 1 times.

 R = 1 times.

We can the number of permutation to arrange this letter with the help of :

nPr = n! / (n - r)!

nPr = Permutation

n = Total number of objects

r = Number of objects selected

'!'     =     Factorial

Factorial :

Factorial (noted as “!”) is the product of all positive integers less than or equal to the number preceding the factorial sign. For example, 3! = 1 x 2 x 3 = 6.

So, nPr  =  9!/(4!) (3!) (1!) (1!)

              = (9×8×7×6×5×4×3×2×1)/(4×3×2×1)×(3×2×1)×(1)×(1)

              = 3,62,880/ 24×6×1×1

              = 3,62,880/144

              = 2,520

Hence, 2520 permutations can be formed from the word 'SASSAFRAS'.

To learn more about Permutation visit :

brainly.com/question/14767366

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