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How many total arrangements can be made using all letters of the following Words?

(1) STATISTICS

(2) BOOKKEEPER

(3) APPEARING

1 Answer

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(1) STATISTICS

In this word there are lo letters of which I is repeated 2 times. S is repeated 3 times and T is repeated 3 times.

Here, n = 10: p = 2; q = 3; r = 3

∴ Total permutation

(2) BOOKKEEPER

According to permutation of Identical things,

Total permutations = \(\frac{n!}{p!q!r!}\)

Here, n = 10; p = 3; q = 2; r = 2

∴ Total permutations

(3) APPEARING

There are 9 letters in this word of which A is repeated 2 times and P is repeated 2 times.

AccordIng to permutation of identical things.

Total permutations = \(\frac{n!}{p!q!}\)

Here, n = 9; p = 2; q = 2

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