# Counting Problem : A code consists of at-most two....

• 22990atinesh
In summary, the number of distinct codes that can be generated using the given criteria is less than 2000. The variables in question are the choice of letter (26), number of identical letters (2), choice of digit (9), and number of identical digits (4). The correct answer may be lower than expected due to the limited number of digits to choose from.
22990atinesh

## Homework Statement

A code consists of at-most two identical letters followed by at-most four identical digits. The code must have atleast one letter and one digit. How many distinct codes can be generated using letters A-Z and digits 1-9.

## The Attempt at a Solution

//One letter followed by one or more digits
##26 \times 10 + 26 \times 10 \times 10 + 26 \times 10 \times 10 \times 10 + 26 \times 10 \times 10 \times 10 \times 10 + ##

//two letters followed by one or more digits
##26 \times 26 \times 10 + 26 \times 26 \times 10 \times 10 + 26 \times 26 \times 10 \times 10 \times 10 + 26 \times 26 \times 10 \times 10 \times 10 \times 10##

But the ans is too big it doesn't matches with the result. What can be correct answer

Your question says identical letters and digits.
So the variables in question are:
Choice of letter (26)
Number of identical letters (2)
Choice of digit (9)
Number of identical digits (4).

Doing it this way, I get an answer that is less that 2000. What are you comparing against?

Two letter cases are still just 26 x 10 ... not 26 x 26 x 10 ... , since the two letters are identical.

22990atinesh said:
using letters A-Z and digits 1-9.
There are only 9 digits to choose from.

## 1. How do I approach solving a counting problem?

When solving a counting problem, it is important to first identify the key elements of the problem such as the total number of options, any restrictions or conditions, and the desired outcome. Once these elements are identified, you can then use various counting techniques such as permutation, combination, or the fundamental counting principle to solve the problem.

## 2. What is the fundamental counting principle?

The fundamental counting principle states that if there are m ways to do one task and n ways to do a second task, then there are m x n ways to do both tasks together. In other words, the total number of outcomes is equal to the product of the number of options for each task. This principle is commonly used in solving counting problems.

## 3. What is the difference between permutation and combination?

Permutation refers to the arrangement of objects in a specific order, while combination refers to the selection of objects without considering the order. In other words, permutation takes into account the order of the objects, while combination does not.

## 4. How do I handle restrictions or conditions in a counting problem?

If a counting problem has restrictions or conditions, it is important to carefully consider how these restrictions affect the total number of options. In some cases, you may need to use the multiplication or addition principle, or even solve multiple smaller counting problems in order to account for the restrictions.

## 5. Can you give an example of a counting problem?

One example of a counting problem is: A code consists of at-most two letters followed by at-most two numbers. How many different codes can be formed if no letter or number can be repeated? In this problem, the key elements are the total number of letters and numbers, as well as the restriction on repetition. Using the multiplication principle, we can determine that there are 26 x 25 x 10 x 9 = 58,500 possible codes that can be formed.

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