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Leslie has been given the task to write either 2-letter words or 2 digit numbers. How many unique numbers or words are possible if repetition of alphabets or digits are not allowed?
- a)70
- b)90
- c)650
- d)731
- e)740
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Leslie has been given the task to write either 2-letter words or 2 dig...
Step 1: Understand the objective
The objective of the question is to list down unique two-digit integers or two-letter words.
The information that can be deduced from the given question is:
- Leslie can use either the digits from 0 to 9 or the alphabets A to Z to complete this activity.
- Repetition of digits or alphabets is not allowed.
Step 2: Write the objective equation enlisting all tasks
Since Leslie has to make a two-digit numbers or a two-letter words, the objective comprises of the following:
- Task 1 – Form two-digit numbers using different digits
- Task 2 – Form two-letter words using different alphabets
Now, in order to accomplish the objective, Leslie can write use either 2-digits OR 2-alphabets.
Therefore, we will put an addition sign in the Objective Equation as under:
Step 3: Determine the number of ways of doing each task
- Task 1 -Form two-digits numbers using digits 0 to 9.
- The number will have two different digits: one digit at the tens place and one digit at the units place.
- Now, all the 10 digits from 0 to 9 are available to us to form the 2-digit numbers.
- However, for the tens digit, we cannot choose 0 (Because a number like 09 or 02 is not a 2-digit integer, but a single digit integer)
- Therefore, for the tens digit, we can only choose from one of the digits between 1 and 9, inclusive.
- Thus, the number of ways in which the tens digit can be chosen = 9
- After one digit has been used up at the tens place, only 9 digits remain available (including 0) for the units place.
- Therefore, the number of ways in which the units digit can be chosen=9
- In order to form the two-digit numbers, we need to fill both the tens digit AND the units digit. Therefore, we will put a multiplication sign between the number of ways of filling these two places.
- Thus, Number of 2-digit numbers possible = 9*9 = 81
- Thus, there are 81 ways to do Task 1.
- Task 2 – Form two-letter words using alphabets A to Z.
- Here we have all the letters from A to Z at our disposal.
- Thus, the first place can be filled in 26 ways (anything from A to Z)
- Now that we have used one of the letters, we have 25 alphabets left.
- Since repetition of alphabets are not allowed.
- Therefore, the second place can be filled in 25 ways.
- Now, in order to form the two-letter words, we need to fill both the first place AND the second place. Therefore, we will put a multiplication sign between the number of ways of filling these two places.
- Thus, Number of 2-letter words possible = 26*25 = 650
- Thus, there are 650 ways to do Task 2
Step 4: Calculate the final answer
Now we can plug the values in the objective equation:
- Total number of different numbers or words which can be written by Leslie = 650 + 81 = 731
- So, there are 731 number of different two-digit numbers or two-letter words that can be formed if repetition is not allowed.
Correct Answer: Option D
Most Upvoted Answer
Leslie has been given the task to write either 2-letter words or 2 dig...
Understanding the Problem
Leslie needs to create either 2-letter words or 2-digit numbers without repeating any letters or digits. Let's break this down into two parts: the 2-letter words and 2-digit numbers.
Calculating Unique 2-Letter Words
- The English alphabet has 26 letters.
- For the first letter, Leslie has 26 choices.
- After selecting the first letter, only 25 letters remain for the second letter.
Formula for 2-Letter Words
- Total 2-letter combinations = 26 (first letter) * 25 (second letter)
= 650 unique 2-letter words.
Calculating Unique 2-Digit Numbers
- The digits range from 0 to 9, giving us 10 options.
- For the first digit, Leslie has 10 choices (0 through 9).
- After selecting the first digit, 9 choices remain for the second digit.
Formula for 2-Digit Numbers
- Total 2-digit combinations = 10 (first digit) * 9 (second digit)
= 90 unique 2-digit numbers.
Final Calculation
- Now, we combine the total unique combinations of 2-letter words and 2-digit numbers:
Total combinations = 650 (2-letter words) + 90 (2-digit numbers)
= 740 unique combinations.
Conclusion
Thus, the total number of unique 2-letter words and 2-digit numbers Leslie can create without repetition is 740. Hence, the correct answer is option D.
Leslie needs to create either 2-letter words or 2-digit numbers without repeating any letters or digits. Let's break this down into two parts: the 2-letter words and 2-digit numbers.
Calculating Unique 2-Letter Words
- The English alphabet has 26 letters.
- For the first letter, Leslie has 26 choices.
- After selecting the first letter, only 25 letters remain for the second letter.
Formula for 2-Letter Words
- Total 2-letter combinations = 26 (first letter) * 25 (second letter)
= 650 unique 2-letter words.
Calculating Unique 2-Digit Numbers
- The digits range from 0 to 9, giving us 10 options.
- For the first digit, Leslie has 10 choices (0 through 9).
- After selecting the first digit, 9 choices remain for the second digit.
Formula for 2-Digit Numbers
- Total 2-digit combinations = 10 (first digit) * 9 (second digit)
= 90 unique 2-digit numbers.
Final Calculation
- Now, we combine the total unique combinations of 2-letter words and 2-digit numbers:
Total combinations = 650 (2-letter words) + 90 (2-digit numbers)
= 740 unique combinations.
Conclusion
Thus, the total number of unique 2-letter words and 2-digit numbers Leslie can create without repetition is 740. Hence, the correct answer is option D.
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Leslie has been given the task to write either 2-letter words or 2 digit numbers. How many unique numbers or wordsare possible if repetition of alphabets or digits are not allowed?a)70b)90c)650d)731e)740Correct answer is option 'D'. Can you explain this answer?
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