4 -letter words'' are formed using the letters A, B, C, D, E, F, G. How many such words are possible for each of the following conditions?(a) No condition is imposed.Your answer is : (b) No letter can be repeated in a word.Your answer is : (c) Each word must begin with the letter A.Your answer is : (d) The letter C must be at the end.Your answer is : (e) The second letter must be a vowel.Your answer is :

(a) No condition is imposed:

The total number of 4-letter words that can be formed from 7 letters is 7^4 = 2401. This is because for each of the 4 positions in the word, there are 7 possible letters that can be chosen.

(b) No letter can be repeated in a word:

The total number of 4-letter words that can be formed from 7 letters without repetition is 765*4 = 840. This is because for the first position there are 7 possible letters, for the second position there are 6 remaining letters, for the third position there are 5 remaining letters, and for the fourth position there are 4 remaining letters.

(c) Each word must begin with the letter A:

The total number of 4-letter words that can be formed from 7 letters where the first letter is A is 177*7 = 343. This is because the first position is fixed as A, and for each of the remaining 3 positions, there are 7 possible letters.

(d) The letter C must be at the end:

The total number of 4-letter words that can be formed from 7 letters where the last letter is C is 777*1 = 343. This is because the last position is fixed as C, and for each of the first 3 positions, there are 7 possible letters.

(e) The second letter must be a vowel:

Assuming the vowels are A and E, the total number of 4-letter words that can be formed from 7 letters where the second letter is a vowel is 727*7 = 686. This is because for the first position there are 7 possible letters, for the second position there are 2 possible vowels, and for each of the remaining 2 positions, there are 7 possible letters.