The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word 'EXAMINATION' is \_\_\_\_\_\_\_.
Answer: 2454
Solutions · 1
Official solution
EXAMINATION: letters N\times 2, A\times 2, I\times 2, and E,X,M,T,O once each.
Case 1: All 4 different. Choose and arrange 4 of the 8 distinct letters: 8P4=1680
Case 2: Two same, two different. Choose the repeated letter (3 choices: N,A,I), choose 2 distinct from remaining 7: (27), arrange: 2!4!:
\[3\times21\times12 = 756\]
Case 3: Two pairs of same letters. Choose 2 of the 3 repeatable letters: (23), arrange: 2!2!4!:
\[3\times6 = 18\]
\[\text{Total} = 1680+756+18 = 2454\]