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Permutation Formulas

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Among certain number of things, if few things are chosen by considering the order of arrangement, then it is known as Permutations. Permutation is of two types. Permutations where repetition is allowed and Permutations where repetition is not allowed. Considering the order of arrangement, if from ‘n’ number of things ‘r’ things are chosen with repetition being allowed, then the number of permutations possible is nr, and if repetition is not allowed, then the number of permutations if given by, nPr = n!/ (n – r)!.
Examples: From the set of 10 numbers, {0, 1, 2… 9}, 4 numbers are chosen. How many permutations are possible?

In order to choose 4 numbers, there are 10 numbers given.

Since repetition is allowed, while choosing the first number there are 10 possibilities.

While choosing the second number, there are again 10 possibilities or choices to choose from!

Similarly, for the third and fourth numbers, there are 10 possibilities each time.

This implies that the number of permutations possible = nr = 104 = 10 * 10 * 10 * 10 = 10,000 permutations.
Example 2: If out of 6 pencils, 3 pencils are to be picked without repetition and considering order of arrangement, then how many permutations are possible?

If there are ‘n’ number of things to choose from, and ‘r’ things are to be selected where repetition is not

allowed and considering the order of arrangement, then the Permutations formulas is given by: nPr = n!/ (n –

So, given n = 6 pencils and r = 3 pencils.

nPr = 6!/ (6 – 3)!

==> 6!/ 3! = 6 * 5 * 4 = 120 permutations.

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