How can I create a strong password to protect my online accounts?

  • MHB
  • Thread starter Asawira Emaan
  • Start date
In summary, the conversation discusses how to calculate the total number of arrangements for the word "equation" with all vowels kept together. The formula for this is n! x (m+1), where n is the number of letters in the group and m is the number of remaining letters. In this case, n=4 and m=3, resulting in a total of 144 possible arrangements. The significance of keeping the vowels together is that it creates a specific pattern, making it easier to calculate. This question can be solved using both combinatorics and permutations, with both approaches resulting in the same answer of 144 possible arrangements.
  • #1
Asawira Emaan
12
0
Asalamoalikum,

Kindly can someone solve these with explanation?

1. In how many ways can four French books, two English books and three German books be arranged on a shelf so that all books in same language are together.

2. How many different arrangements can be formed of the word "equation" if all the vowels are to be kept together?

3. A combination lock has five wheels, each labeled with the ten digits from 0 to 9. How many five number opening combinations are possible,
(i) assuming no digit is repeated.
(ii)assuming digits can be repeated.

Thank you.
 
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  • #2
Asawira Emaan said:
Asalamoalikum,

Kindly can someone solve these with explanation?
You won't learn anything by people doing your homework for you! Here are some hints:

1. In how many ways can four French books, two English books and three German books be arranged on a shelf so that all books in same language are together.
First, treat the books of each language, which must be kept together, as one object. In how many ways can you arrange 3 objects? Now, in how many ways can you arrange just the 4 French books? The two English books? The three German books? By the "fundamental counting principle", multiply those.

2. How many different arrangements can be formed of the word "equation" if all the vowels are to be kept together?
Treat the vowels, e, u a, i, and o, that are to be kept together, as a single letter. there are also 3 consonants so, treating the vowels as a single letter, there are 4 objects. In how many ways can you arrange 4 objects. In how many ways can you arrange the 5 vowels?

3. A combination lock has five wheels, each labeled with the ten digits from 0 to 9. How many five number opening combinations are possible,
(i) assuming no digit is repeated.
There are 10 choices for the first digit, then 9 for the second, etc.

(ii)assuming digits can be repeated.
Then there are 10 choices for every digit.

Thank you.
 
  • #3
Country Boy said:
You won't learn anything by people doing your homework for you! Here are some hints:First, treat the books of each language, which must be kept together, as one object. In how many ways can you arrange 3 objects? Now, in how many ways can you arrange just the 4 French books? The two English books? The three German books? By the "fundamental counting principle", multiply those. Treat the vowels, e, u a, i, and o, that are to be kept together, as a single letter. there are also 3 consonants so, treating the vowels as a single letter, there are 4 objects. In how many ways can you arrange 4 objects. In how many ways can you arrange the 5 vowels?There are 10 choices for the first digit, then 9 for the second, etc.Then there are 10 choices for every digit.
Thanks by the time I got this answer I had already done the homework.
 
  • #4
Good! That's the way it should be!
 

1. How long should my password be?

A strong password should be at least 12 characters long. The longer the password, the harder it is for hackers to guess or crack it.

2. Should I use a combination of letters, numbers, and special characters?

Yes, a strong password should contain a combination of lowercase and uppercase letters, numbers, and special characters. This makes it more difficult for hackers to guess or use automated programs to crack your password.

3. Can I use the same password for multiple accounts?

No, it is not recommended to use the same password for multiple accounts. If one account gets hacked, all of your accounts are at risk. It is best to use unique passwords for each account.

4. How often should I change my password?

It is recommended to change your password every 3-6 months. This reduces the risk of your password being compromised and gives you a chance to create a new, strong password.

5. Is it safe to use password managers?

Yes, password managers can be a safe and convenient way to store and manage your passwords. Just make sure to choose a reputable password manager and use a strong master password to protect your account.

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