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Formula of Permutation – how to solve correctly?

Here is the Formula of Permutation

In SAT Math you may come across a Permutation Problem which you solve by using above Formula of Permutation. This is right approach. But sometimes this Formula returns wrong answer. How is it possible? How to obtain correct answer? It is quite easy to reach correct answer. See following example.

Example

How many word strings can be formed by rearranging the letters of word SUCCESS?

Solution

First check whether order matters? SUCCESS and CUSSESC both are different word strings. It means that order matters here. It is a problem of math Permutation.

You are to rearrange 7 letters of SUCCESS in group of 7 new word strings. So n = 7, r = 7. If you put these values in above Formula of Permutation, you’ll have 0! in denominator (0! = 1) and the answer will be

nPr = 7!

= 7x6x5x4x3x2x1

= 5040

If you chose this answer, then you are making blunder as this is wrong answer. In fact, you have ignored one more fact while solving Permutation equation. This fact is presence of indistinguishable objects of C and S in the word SUCCESS. There is repetition of 2 C’s and 3 S’s in word SUCCESS. Now take into account this repetition and write and solve Permutation equation correctly.

Remember, in permutation Problems where there is repetition of indistinguishable objects, basic Formula of Permutation nPr is divided by factorial of these number of repetitions.

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