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. (b) No letter can be repeated in a word. (c) Each word must begin with the letter A (d) The letter C must be at the end. (e) The second letter must be a vowel.

I think its E

the second letter must be a vowel

Answer: a) 2401 b) 840 c) 343 d) 343 e) 686

Step-by-step explanation:

a) Total are 7 letters

There are 4 possible places in 4-letter word for each of 7 letter.

So total amount of the words is

7*7*7*7 = 2401

b) No letter can be repeated mens that in 1st place can stay any of 7 letters,

in 2-nd place - any of 6 letters

in 3-rd place - any of 5 letters

in 4-th place any of 4 letters

Total amount of words is

7*6*5*4=840

c) It is not written if the letters can be repeated. Assume that they can.

1st place occupied by letter A. So at 2-nd, 3-rd and 4th places can stay any of 7 letters

Total amount of words is

1*7*7*7=343

d) Similar case like c). At 1-st, 2-nd, 3-rd can stay any of 7 letters, and at 4th place the letter C (1 letter). Total amount of words is

7*7*7*1=343

e) There are 2 vowels A and E.

So at 1st place can stay any of 7 letters, at 2-nd place - any of 2 letters, at 3-rd place - any of 7 letters and at 4th place any of 7 letters. Total amount of words is

7*2*7*7=686