Question

Which of the following expressions shows the number of 8 character passwords that can be formed using letters and digits if the password must begin with a letter? a. 21 times 36 superscript 7 b. 26 times 36 superscript 7 c. 26 superscript 5 baseline times 10 superscript 3 d. 36 superscript 8.

Answer 1

The number of 8 character passwords that can be formed using letters and digits if the password must begin with a letter is 26×31⁷.

What is Combination?

The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.

$^nC_r = \dfrac{n!}{r!(n-r)!}$

where,

n is the number of choices available,

r is the choices to be made.

As it is given that the password can only be made with letters or numbers, and we know that there are only 26 letters and there are 10 numbers, therefore, the total option available is 36.

Also, it is given that the first letter of the password can only be made with letters, therefore, there are only 26 options available for the first place in the password.

The number of 8 character passwords that can be formed using letters and digits if the password must begin with a letter,

$= ^{26}C_{1} \times ^{36}C_{1} \times ^{36}C_{1} \times ^{36}C_{1} \times ^{36}C_{1} \times ^{36}C_{1} \times ^{36}C_{1} \times ^{36}C_{1} \\\\= 26 \times 31\times 31\times 31\times 31\times 31\times 31\times 31\\\\= 26 \times 31^7$

Hence, the number of 8 character passwords that can be formed using letters and digits if the password must begin with a letter is 26×31⁷.

Learn more about Combination:

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