Technology Combinatorics

Probability Level pending

How many words can be made with the letters of the word "TECHNOLOGY" which do not begin with "T" but end with "Y" ?

Solve more problems like this in my set Combinatorics


The answer is 161280.

Nikhil Ramakrishnan by Nikhil Ramakrishnan , 22, India

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1 solution

Let's say we have fixed "Y" in the last place.

Then, number of ways in which the other alphabets can be arranged is given by:

9 ! 2 ! \frac{9!}{2!} (∵ "O" is repeated twice)

Now, we will subtract the cases in which "T" occurs in the first place (with Y still fixed in the last). This is given by:

8 ! 2 ! \frac{8!}{2!}

Subtracting,

9 ! − 8 ! 2 ! \frac{9! - 8!}{2!} = 161280 = 161280

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