If a password consists of 3 letters followed by 2 digits, how many different pas
Practice Questions
Q1
If a password consists of 3 letters followed by 2 digits, how many different passwords can be formed using the first 3 letters of the alphabet and the first 5 digits?
150
180
120
100
Questions & Step-by-Step Solutions
If a password consists of 3 letters followed by 2 digits, how many different passwords can be formed using the first 3 letters of the alphabet and the first 5 digits?
Step 1: Identify the letters and digits available. We have the first 3 letters of the alphabet: A, B, C. We also have the first 5 digits: 0, 1, 2, 3, 4.
Step 2: Calculate the number of ways to arrange the 3 letters. Since we have 3 letters and we want to use all of them, we can arrange them in 3! (3 factorial) ways. 3! = 3 × 2 × 1 = 6.
Step 3: Calculate the number of ways to choose and arrange 2 digits from the 5 available digits. This is done using permutations since the order matters. The formula for permutations is 5P2, which is calculated as 5! / (5-2)! = 5 × 4 = 20.
Step 4: Multiply the number of arrangements of letters by the number of arrangements of digits to find the total number of different passwords. Total = 3! × 5P2 = 6 × 20 = 120.
Permutations and Combinations – The question tests the understanding of how to calculate the number of arrangements of letters and digits using permutations and combinations.
Factorials – The use of factorials to determine the number of ways to arrange the letters is a key concept in combinatorial mathematics.
