icense plate begins with three letters. If the possible letters are A, B, C, D and E, how many different permutations of these letters can be made if no letter is used more than once?
Solution:
Using reasoning:
For the first letter, there are 5 possible choices. After that letter is chosen, there are 4 possible choices. Finally, there are 3 possible choices.
5 × 4 × 3 = 60
Using the permutation formula:
The problem involves 5 things (A, B, C, D, E) taken 3 at a time.
Example:
In how many ways can a president, a treasurer and a secretary be chosen from among 7 candidates?
Solution:
Using reasoning:
For the first position, there are 7 possible choices. After that candidate is chosen, there are 6 possible choices. Finally, there are 5 possible choices.
7 × 6 × 5 = 210
Using the permutation formula:
The problem involves 7 candidates taken 3 at a time.
There are 210 possible ways to choose a president, a treasurer and a secretary be chosen from among 7 candidates
Step-by-step explanation:
What are the real-life examples of permutations and combinations? Arranging people, digits, numbers, alphabets, letters, and colours are examples of permutations. Selection of menu, food, clothes, subjects, the team are examples of combinations.
Answers & Comments
Answer:
icense plate begins with three letters. If the possible letters are A, B, C, D and E, how many different permutations of these letters can be made if no letter is used more than once?
Solution:
Using reasoning:
For the first letter, there are 5 possible choices. After that letter is chosen, there are 4 possible choices. Finally, there are 3 possible choices.
5 × 4 × 3 = 60
Using the permutation formula:
The problem involves 5 things (A, B, C, D, E) taken 3 at a time.
Example:
In how many ways can a president, a treasurer and a secretary be chosen from among 7 candidates?
Solution:
Using reasoning:
For the first position, there are 7 possible choices. After that candidate is chosen, there are 6 possible choices. Finally, there are 5 possible choices.
7 × 6 × 5 = 210
Using the permutation formula:
The problem involves 7 candidates taken 3 at a time.
There are 210 possible ways to choose a president, a treasurer and a secretary be chosen from among 7 candidates
Step-by-step explanation:
What are the real-life examples of permutations and combinations? Arranging people, digits, numbers, alphabets, letters, and colours are examples of permutations. Selection of menu, food, clothes, subjects, the team are examples of combinations.