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1. Given 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

1. Given 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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pls answer 1-3 on paper, thank you

Counting Techniques Test your understanding Apply the appropriate counting technique to solve for the following. 1. Given 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? 2. A basketball team is composed of 10 players. How many different selections are there if we are going to select a 5-member starting line-up and a team captain? 3. How many ways can 10 persons sit in a round table if two of them always sit together? 4. If a license plate pattern is LLL NNNN where L is a letter and N is a number digit, how many possible license plates can be issued? 5. How many possible iterations are there for the letters in the word mississippi? 6. How many possible winning numbers are there in a 6/45 lottery? 7. How many 3-digit numbers can be formed from the set of decimal digits if the numbers formed are all even numbers and repetition of digits is not allowed? 8. How many subsets of length 5 are there for the set of consonants of the English alphabet? 9. A box contains 5 red balls, 4 green balls, and 7 blue balls. How many ways can we pick 2 balls with different colors? 10. On a typical keyboard, there are 26 small cap letters, 26 uppercase letters, 10 decimal digits, and 33 special characters. How many possible passwords 9 characters long can be generated using these options on the keyboard if a character can only be used once?
Transcribed Image Text:Counting Techniques Test your understanding Apply the appropriate counting technique to solve for the following. 1. Given 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? 2. A basketball team is composed of 10 players. How many different selections are there if we are going to select a 5-member starting line-up and a team captain? 3. How many ways can 10 persons sit in a round table if two of them always sit together? 4. If a license plate pattern is LLL NNNN where L is a letter and N is a number digit, how many possible license plates can be issued? 5. How many possible iterations are there for the letters in the word mississippi? 6. How many possible winning numbers are there in a 6/45 lottery? 7. How many 3-digit numbers can be formed from the set of decimal digits if the numbers formed are all even numbers and repetition of digits is not allowed? 8. How many subsets of length 5 are there for the set of consonants of the English alphabet? 9. A box contains 5 red balls, 4 green balls, and 7 blue balls. How many ways can we pick 2 balls with different colors? 10. On a typical keyboard, there are 26 small cap letters, 26 uppercase letters, 10 decimal digits, and 33 special characters. How many possible passwords 9 characters long can be generated using these options on the keyboard if a character can only be used once?
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