**A-Level ****Mathematics Question Analysis Topic: Mathematics - Permutation**

If the letters of the word PRISON are permutated in all possible ways and the words thus formed are arranged in dictionary order, find the rank of the word PRISON.

**Answer:**

For A-Level Mathematics, you should know:

Total number of letters in PRISON = 6

If all permutations are arranged in alphabetical order, all words beginning with I, N, O, PI, PN, PO, PRIN, PRIO and PRISN will come before PRISON.

Hence,

Number of words starting with:

I = 5! = 120

N = 5! = 120

O = 5! = 120

PI = 4! = 24

PN = 4! = 24

PO = 4! = 24

PRIN = 2! = 2

PRIO = 2! = 2

PRISN = 1! = 1

Total number of words before PRISON is the sum of the above numbers = 437

As such, the rank of PRISON is 438.

Make sure to drill similar questions for your A-Level Mathematics examination!

End of analysis. Great!