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  • A password consists of 4 letters, where each letter can be either a vowel (a, e, i, o, u) or a consonant. In addition, the password must contain exactly two vowels and tw

A password consists of 4 letters, where each letter can be either a vowel (a, e, i, o, u) or a consonant. In addition, the password must contain exactly two vowels and two consonants. How many different passwords are possible?

 

Option: 1

4000


Option: 2

2100


Option: 3

2800


Option: 4

5600


Answers (1)

best_answer

First, let's determine the number of ways to arrange the two vowels in the password. There are 5 vowels to choose from, and we need to select 2 of them. This can be calculated using the combination formula:

\mathrm{C(5,2)=5 ! /(2 ! \times(5-2) !)=10 .}

Similarly, we need to determine the number of ways to arrange the two consonants. There are 21 consonants to choose from (total 26 letters minus the 5 vowels), and we need to select 2 of them. Using the combination formula:

\mathrm{C(21,2)=21 ! /(2 ! \times(21-2) !)=210 .}

Now, we have determined the number of ways to arrange the vowels and the consonants independently. To find the total number of possible passwords, we multiply these two values: 10 \times 210 = 2,100.

Therefore, there are 2,100 different passwords possible.

 

Posted by

sudhir kumar

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