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 :
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 :
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.CT: Chapter Test
Problem 3CT: An Internet service provider requires its customer to select a password consisting of four letters...
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Transcribed Image Text: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 :
Expert Solution
Step 1
4-letter words are to be formed form the letters A, B, C, D, E, F, G.
We have in all 7 letters.
Part a: No condition is imposed
We can select the first letter in 7 ways, second letter in 7 ways, third letter in 7 ways and the fourth letter in 7 ways.
Thus, the number of words formed when no condition is imposed is 7 × 7 × 7 × 7 = 2401.
Part b: No letter can be repeated in the word.
We can select the first letter in 7 ways, second letter in 6 ways, third letter in 5 ways and the fourth letter in 4 ways.
Thus, the number of words formed when no letter can be repeated in the word is 7 × 6 × 5 × 4 = 840.
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