A4- figure passcode is to be formed from 3 letters of the alphabet and 3 digits. how many passcodes can be formed if: a. the first figure is a letter and the rest are digitsb. the first and last figures are digits and in the middle is letter dc. the digits and alphabets are alternate

A. 81

B. 9

C. 81

Step-by-step explanation:

We have that,

Number of figures in the password = 4.

Number of letters used = 3

Number of digits used = 3.

A. The first figure is a letter and the rest are digits

As, the first figure is a letter, so its position is fixed and the other figure are the numbers.

Since, there can be any possibility out of 3 letters and 3 digits,

Number of ways to form the pass-code = 3 × 3 × 3 × 3 = 81

Thus, there are 81 ways in this case.

B. The first and last figure are digits and in the middle is the letter D.

So, we have the case,  _ D D _ with the blanks taking digits.

Since, there can be any possibility out of 3 digits,

Number of ways to form the pass-code = 3 × 1 × 1 × 3 = 9

Thus, there are 9 ways in this case.

C. The digits and alphabets are alternate.

As, there are 3 options for letters and 3 options for digits.

Number of ways to form the pass-code = 3 × 3 × 3 × 3 = 81

Thus, there are 81 ways in this case.