SOLUTION: find the number of ways of selecting four letters from the word 'EXAMINATION'.ANSWER IS 136 PLS SOLVE THIS THANK U

Question 658654: find the number of ways of selecting four letters from the word 'EXAMINATION'.ANSWER IS 136 PLS SOLVE THIS THANK U
Found 2 solutions by MathLover1, kevwill:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
EXAMINATION has letters, and in which '', '' and '', all occur twice. , would have been fine if all letters were distinct.
So, we have,, , , , (), (), ()... distinct letters.
1. letters selected, which are distinct:
2. letters alike, and distinct (eg: ) =
3. letters alike, and letters alike (eg: ) =
So answer is,.
Answer by kevwill(135) (Show Source): You can put this solution on YOUR website!
Actually, the answer is 131.
For an excellent, detailed description of the theory behind the solution, please see http://mathforum.org/library/drmath/view/56197.html
I sorted the letters of the word EXAMINATION by frequency of occurrence to get AAIINNEMOTX. That told me we are looking for the number of 4-combinations of the set (2,2,2,1,1,1,1,1).
We can use the generating function and find the coefficient of the resulting term.
When multiplied out, the expanded generating function is:
and the coefficient of the term is 131. Thus, there are 131 ways to select four letters from the word "EXAMINATION"

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