(5 points) If 5 -letter words\" are formed using the letters A, B, C, D, E, F, G

Question

(5 points) If 5 -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 repeatec. Your answer is

Explanation / Answer

(a) There are 5 letters and each letter has 7 choices.

Number of words = 75 = 16807.

(b) The first letter can come in 7 ways, the second letter in 6 ways and so on.

Number of words = 7*6*5*4*3 = 2520.

(c) There is only one choice for the first letter. The remaining letters can come in 74 ways.

Number of words = 74 = 2401.

(d) There is only one choice for the last letter. The remaining letters can come in 74 ways.

Number of words = 74 = 2401.

(e) The second letter has two choices namely A and E. The remaining letters can come in 74 ways.

Number of words = 2 * 74 = 4802.

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