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Chapter 11: Problem 51

How many distinct permutations can be formed using the letters of the word TALLAHASSEE?

Short Answer

Expert verified
The number of distinct permutations that can be formed from the word 'TALLAHASSEE' is calculated as \[ \frac{{11!}}{{1!*3!*2!*2!*2!*1!}} \]. Calculate this value to get the result. The final answer will depend on the mathematical calculation of these factorials.

Step by step solution

01

Identify the Letters & Their Frequency

The letters in the word 'TALLAHASSEE' are: one 'T', three 'A', two 'L', two 'S', two 'E' and one 'H'. So, the frequency of the letters in the word are: \nT - 1\nA - 3\nL - 2\nS - 2\nE - 2\nH - 1
02

Count Total Number of Letters

The total number of letters in the word 'TALLAHASSEE' is 11.
03

Number of Distinct Permutations

The formula to find the number of distinct permutations for a set of items where some items are repeated is given by: \[ \frac{{n!}}{{n1!*n2!*n3!* ... * nk!}} \] Where, \n n = total number of items,\n n1, n2, n3, ... nk = number of each repeated item.\n Applying this formula for the letters in the word 'TALLAHASSEE' we get, \[ \frac{{11!}}{{1!*3!*2!*2!*2!*1!}} \]
04

Calculate The Result

Calculate the factorial for each of the values and substitute them in the equation. This will give us the number of distinct permutations that can be formed from the word 'TALLAHASSEE'

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