Question

How many permutations of 4 letters can be made out of the letters of the word "EXAMINATION"?

Answer 1

\[\frac{ {_{11}P_{4}} }{2!*2! } = 1980 \]

Answer 2

"EXAMINATION"

Total 11 letters, 1E,1X,2A,1M,2I,2N,1O,1T, the answer is the coefficient of \(x^4\) in \[ 4! (1+x)^5 (1+x+\frac {x^2}{2!})^3 \] which is \(2454 \)