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)
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Chapter1: Combinatorial Analysis
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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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