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A user wants to create a password using 4 lowercase letters (a-z) and 3 uppercase letters (A-Z). No letter can be repented in any form. In how many ways can the password be created if the password must start with an uppercase letter?
(a) 26 x 25 x 24 x 23 x 22 x 5 x 21
(b) 26 x 25 x 24 x23 × 22 × 2 × 21
(c) 26 × 5 × 25 × 24 × 23 × 2 × 22 × 21
(d) 6 × 26 × 25 × 24 × 23 × 22 × 21?
(a) 26 x 25 x 24 x 23 x 22 x 5 x 21
(b) 26 x 25 x 24 x23 × 22 × 2 × 21
(c) 26 × 5 × 25 × 24 × 23 × 2 × 22 × 21
(d) 6 × 26 × 25 × 24 × 23 × 22 × 21?
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A user wants to create a password using 4 lowercase letters (a-z) and ...
Understanding Password Requirements
To create a password consisting of 4 lowercase letters and 3 uppercase letters, with the condition that it starts with an uppercase letter and no letters can be repeated, we need to analyze the structure of the password.
Structure of the Password
- The password has a total of 7 characters: 1 uppercase letter (first character) + 4 lowercase letters + 2 uppercase letters.
- Since it must start with an uppercase letter, our first choice is an uppercase letter followed by lowercase letters.
Ways to Choose Uppercase Letters
- The first character of the password can be any of the 26 uppercase letters.
- After selecting the first uppercase letter, there are 25 uppercase letters left for the second uppercase letter.
Ways to Choose Lowercase Letters
- We then need to select 4 lowercase letters from the 26 available.
- The first lowercase letter can be chosen from 26 options, the second from 25, the third from 24, and the fourth from 23.
Calculating Total Combinations
Putting this together, the total number of ways to create the password is calculated as follows:
- Choices for the first uppercase letter: 26
- Choices for the second uppercase letter: 25
- Choices for the first lowercase letter: 26
- Choices for the second lowercase letter: 25
- Choices for the third lowercase letter: 24
- Choices for the fourth lowercase letter: 23
Thus, the calculation is:
- Total Combinations = 26 (1st uppercase) * 25 (2nd uppercase) * 26 (1st lowercase) * 25 (2nd lowercase) * 24 (3rd lowercase) * 23 (4th lowercase)
Hence, the total number of ways to create the password while following these rules is represented mathematically by:
- 26 x 25 x 24 x 23 x 22 x 25 x 24 x 23.
The correct option that aligns with this calculation is option (a).
To create a password consisting of 4 lowercase letters and 3 uppercase letters, with the condition that it starts with an uppercase letter and no letters can be repeated, we need to analyze the structure of the password.
Structure of the Password
- The password has a total of 7 characters: 1 uppercase letter (first character) + 4 lowercase letters + 2 uppercase letters.
- Since it must start with an uppercase letter, our first choice is an uppercase letter followed by lowercase letters.
Ways to Choose Uppercase Letters
- The first character of the password can be any of the 26 uppercase letters.
- After selecting the first uppercase letter, there are 25 uppercase letters left for the second uppercase letter.
Ways to Choose Lowercase Letters
- We then need to select 4 lowercase letters from the 26 available.
- The first lowercase letter can be chosen from 26 options, the second from 25, the third from 24, and the fourth from 23.
Calculating Total Combinations
Putting this together, the total number of ways to create the password is calculated as follows:
- Choices for the first uppercase letter: 26
- Choices for the second uppercase letter: 25
- Choices for the first lowercase letter: 26
- Choices for the second lowercase letter: 25
- Choices for the third lowercase letter: 24
- Choices for the fourth lowercase letter: 23
Thus, the calculation is:
- Total Combinations = 26 (1st uppercase) * 25 (2nd uppercase) * 26 (1st lowercase) * 25 (2nd lowercase) * 24 (3rd lowercase) * 23 (4th lowercase)
Hence, the total number of ways to create the password while following these rules is represented mathematically by:
- 26 x 25 x 24 x 23 x 22 x 25 x 24 x 23.
The correct option that aligns with this calculation is option (a).
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A user wants to create a password using 4 lowercase letters (a-z) and 3 uppercase letters (A-Z). No letter can be repented in any form. In how many ways can the password be created if the password must start with an uppercase letter?(a) 26 x 25 x 24 x 23 x 22 x 5 x 21(b) 26 x 25 x 24 x23 × 22 × 2 × 21(c) 26 × 5 × 25 × 24 × 23 × 2 × 22 × 21(d) 6 × 26 × 25 × 24 × 23 × 22 × 21?
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A user wants to create a password using 4 lowercase letters (a-z) and 3 uppercase letters (A-Z). No letter can be repented in any form. In how many ways can the password be created if the password must start with an uppercase letter?(a) 26 x 25 x 24 x 23 x 22 x 5 x 21(b) 26 x 25 x 24 x23 × 22 × 2 × 21(c) 26 × 5 × 25 × 24 × 23 × 2 × 22 × 21(d) 6 × 26 × 25 × 24 × 23 × 22 × 21? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A user wants to create a password using 4 lowercase letters (a-z) and 3 uppercase letters (A-Z). No letter can be repented in any form. In how many ways can the password be created if the password must start with an uppercase letter?(a) 26 x 25 x 24 x 23 x 22 x 5 x 21(b) 26 x 25 x 24 x23 × 22 × 2 × 21(c) 26 × 5 × 25 × 24 × 23 × 2 × 22 × 21(d) 6 × 26 × 25 × 24 × 23 × 22 × 21? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A user wants to create a password using 4 lowercase letters (a-z) and 3 uppercase letters (A-Z). No letter can be repented in any form. In how many ways can the password be created if the password must start with an uppercase letter?(a) 26 x 25 x 24 x 23 x 22 x 5 x 21(b) 26 x 25 x 24 x23 × 22 × 2 × 21(c) 26 × 5 × 25 × 24 × 23 × 2 × 22 × 21(d) 6 × 26 × 25 × 24 × 23 × 22 × 21?.
A user wants to create a password using 4 lowercase letters (a-z) and 3 uppercase letters (A-Z). No letter can be repented in any form. In how many ways can the password be created if the password must start with an uppercase letter?(a) 26 x 25 x 24 x 23 x 22 x 5 x 21(b) 26 x 25 x 24 x23 × 22 × 2 × 21(c) 26 × 5 × 25 × 24 × 23 × 2 × 22 × 21(d) 6 × 26 × 25 × 24 × 23 × 22 × 21? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A user wants to create a password using 4 lowercase letters (a-z) and 3 uppercase letters (A-Z). No letter can be repented in any form. In how many ways can the password be created if the password must start with an uppercase letter?(a) 26 x 25 x 24 x 23 x 22 x 5 x 21(b) 26 x 25 x 24 x23 × 22 × 2 × 21(c) 26 × 5 × 25 × 24 × 23 × 2 × 22 × 21(d) 6 × 26 × 25 × 24 × 23 × 22 × 21? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A user wants to create a password using 4 lowercase letters (a-z) and 3 uppercase letters (A-Z). No letter can be repented in any form. In how many ways can the password be created if the password must start with an uppercase letter?(a) 26 x 25 x 24 x 23 x 22 x 5 x 21(b) 26 x 25 x 24 x23 × 22 × 2 × 21(c) 26 × 5 × 25 × 24 × 23 × 2 × 22 × 21(d) 6 × 26 × 25 × 24 × 23 × 22 × 21?.
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