The number of 4 letter word (with or without meaning) that can be formed from the eleven letters of the word 'EXAMINATION is .......

Step-by-step solution

Given word is 'EXAMINATION' having letters (AA), (II), (NN), EXMOT, we have to form 4 letter words, then following cases are possible, (I) 2 same, 2 same and number of words are ^3 C₂ 4! 2!2! =18 (II) 2 same, 2 different and number of words are aligned & ^3 C₁ ^7 C₂ 4! 2! =3 7 6 2 4 3 2 2 & =21 36=756 aligned (III) All are different and number of words are ^8 C₄ 4!= 8 7 6 5 4! 4!=1680 So, total number of 4 letter words 18+756+1680=2454