Final answer:
The number of 4-letter words that can be formed from the word "examination" is 2887 by calculating different permutations based on letter repetitions. None of the multiple choice options provided match this answer.
Step-by-step explanation:
To find the number of 4-letter words that can be formed from the eleven letters of the word "examination", we need to consider the repetitions of letters in the given word. The word "examination" has the following letters: E, X, A, M, I, N, T, O, with 'A' and 'I' each repeating twice and 'N' three times.
When forming 4-letter words, we have to take into account the repetitions:
- If all four letters are different, the number of permutations is 8P4 (permutation of 8 different letters taken 4 at a time).
- If there are two 'A's or two 'I's, the permutations will be 7P3 (permutation of the remaining 7 letters taken 3 at a time) times 2, because there are two different letters which can be repeated.
- If we use two 'N's and two other different letters, it will be 6P2 (permutation of the remaining 6 letters taken 2 at a time).
- If we use three 'N's and one different letter, it will be 7P1 (permutation of the remaining 7 letters taken 1 at a time).
Calculating the number of permutations for each case and summing them up:
- 8P4 = 8!/(8-4)! = 1680
- 7P3 * 2 (for two 'A's or two 'I's) = (7!/(7-3)!)*2 = 840
- 6P2 (for two 'N's) = 6!/(6-2)! = 720/2 = 360, because the two 'N's are indistinguishable.
- 7P1 (for three 'N's) = 7 = 7, same logic as above.
Adding up these permutations gives us a total of 1680 + 840 + 360 + 7 = 2887.
Therefore, the answer is none of the options provided (a) 110 (b) 220 (c) 330 (d) 440. If this is a multiple choice question, it seems there may be an error in the question or in the provided options.