Question

PROBABILITIES!! HELP!!!

A 4- 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 digits
b. The first and last figures are digits and in the middle is letter D
c. The digits and alphabets are alternate

Answer 1

Answer:

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.

Answer 2

There are 54 ways for Combination A, 9 ways for Combination B and 36 ways for Combination C to create the passcode.

What are permutation and combination?

A permutation can be defined as a process of arranging the objects or numbers in order.

Combinations are the way of selecting the objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.

Given that a 4- figure passcode is to be formed from 3 letters of the alphabet and 3 digits.

We need to calculate the permutations for the passcode.

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

The position of the first letter is fixed and the other figures are the numbers. There are 3 options for 2 alphabets (as one is fixed on the first position) and 3 options for 3 digits.

Number of ways to form the passcode = 3 × 2 × 3 × 3

Number of ways to form the passcode = 54

For B: The first and last figures are digits and in the middle is the letter D.

The position of the middle 2 letters is fixed.

Number of ways to form the passcode = 3 × 1 × 1 × 3

Number of ways to form the passcode = 9

For C: The digits and alphabets are alternate

There are 2 options for 3 letters and 2 options for 3 digits.

Number of ways to form the passcode = 2 × 3 × 2 × 3 = 36

Hence we can conclude that there are 54 ways for Combination A, 9 ways for Combination B and 36 ways for Combination C to create the passcode.

To know more about the permutation and combination, follow the link given below.

https://brainly.com/question/11732255.