An anagram is simply a rearrangement of the letters of a word to make a new “wor

Question

An anagram is simply a rearrangement of the letters of a word to make a new “word”. For example, an anagram of DISCRETE is the word DEERSTIC. Note that anagrams don’t need to be actual words in the dictionary. How many anagrams are there of the following words? Find your answer without resorting to “brute force” methods (that is, just listing all the possible anagrams and counting them) but rather use mathematical arguments to count without listing. Be sure to give complete explanations for your answers.

1. MATH

2. DISCRETE

3. PHILADEPLHIA

4. OVERNUMEROUSNESSES

Explanation / Answer

Solution: arrengment of word= (no. of letter)!/(repetition letter)!

1): in the word "math" no. of letter is 4, then arrengment of word=4!=4*3*2*1=24

2): in the word "discrete" no. of letter is 8 & repetetion of e is 2 times, then arrengment of word=8!/2!=20160

3):in the word "philadeplhia" no. of letter is 12, no. of repetetion letter p=2, h=2, i=2, l=2, a=2                                 then arrengment of word=12!(2!*2!*2!*2!*2!)=2138400

4): in the word "overnumerousnesses" no. of letter is 18 & no. of repetetion letter o=2, e=4, r=2, n=2, u=2, s=4 then arrengment of word= 18!(2!*4!*2!*2!*2!*4!)=2.500927229*1013

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