Recall that for the purposes of this class an anagram is sim

Recall that for the purposes of this class, an anagram is simply a rearrangement of the letters of a word and does not need to appear in an English dictionary. For example, “odg” is considered an anagram of the word “dog”.

(a) How many anagrams exist of the word “bogus”?

(b) How many anagrams exist of the word “banana”?

(c) How many anagrams exist of the word “MISSISSIPPI”?

(d) How many anagrams exist of the word “MISSISSAUGA”?

Solution

(a) Bogus has 5 distinct letters. n distinct letters can be arrange n! ways

So bogus can arranged in 5! ways=5*4*3*2*1=120 Anagrams

(b) Banana has 6 letters of which 2 are \"n\" and 3 are \"a\"

So total arrangements = 6!/(3!2!)= 120 Anagrams for \"Banana\"

(c)“MISSISSIPPI” has 11 letters of which 4 are \"s\" , 2 are \"p\" and 4 are \"I\"

So total arrangements = 11!/(4!4!2!) = 34650 Anagrams for \"MISSISSIPPI\"

(d) “MISSISSAUGA” has 11 letters of which 4 are \"s\", 2 are \"A\" 2 are \"I\"

So total arrangements = 11!/(4!2!2!) = 415800 Anagrams for “MISSISSAUGA”