If 3 -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 and letters can be repeated.Your answer is : (d) The letter C must be at the end and letters can be repeated.Your answer is : (e) The second letter must be a vowel and letters can be repeated.Your answer is :

(a) No condition is imposed: There are 7 options for each of the 3 letters, so the total number of words is 777 = 343.

(b) No letter can be repeated in a word: There are 7 options for the first letter, 6 for the second (since it can't be the same as the first), and 5 for the third (since it can't be the same as the first two). So the total number of words is 765 = 210.

(c) Each word must begin with the letter A and letters can be repeated: There is only 1 option for the first letter (A), but 7 options for each of the other two letters. So the total number of words is 177 = 49.

(d) The letter C must be at the end and letters can be repeated: There are 7 options for the first two letters, but only 1 option for the third (C). So the total number of words is 771 = 49.

(e) The second letter must be a vowel and letters can be repeated: There are 7 options for the first letter, 2 options for the second (A, E), and 7 options for the third. So the total number of words is 727 = 98.