A student created a 6 character computer password, the password strts with 4 digits, the first of which is he number 3, followed by 2 letters, the firsr of which is a consonant. How many different passwords are possible if repetition is allowed?
I know its 1x10x10x10x21x26
But is it factorial??
No
No, the calculation you provided is not factorial. To understand why, let's break down the calculation step by step.
The password consists of 6 characters: 4 digits followed by 2 letters.
For the first digit, we are given that it must be the number 3. So, there is only 1 option for this digit.
For the second, third, and fourth digits, any digit from 0 to 9 can be chosen, so there are 10 options for each of these digits.
For the first letter, we are given that it must be a consonant. There are 21 consonants in the English alphabet, so we have 21 options for this letter.
For the second letter, any letter from A to Z can be chosen, so there are 26 options for this letter.
To find the total number of possible passwords, we multiply the number of options for each character:
1 (option for the first digit) × 10 (options for the second digit) × 10 (options for the third digit) × 10 (options for the fourth digit) × 21 (options for the first letter) × 26 (options for the second letter).
Multiplying these numbers together, we get: 1 × 10 × 10 × 10 × 21 × 26 = 546,000.
So, there are 546,000 different possible passwords if repetition is allowed.
This calculation does not involve factorial operations. Factorial is used to calculate the number of permutations when all elements are used without repetition. Here, repetition is allowed, so factorial is not applicable.