There are 26 letters in the alphabet and 10 numbers from 0 to 9.
A password with 6 numbers is less likely to be guessed.
Practice makes perfect
We want to determine which password is less likely to be guessed, a password with six numbers or a password with four capital letters. The more options there are for a password, the less likely it is that the password is guessed. To figure out whether the 4-letter password is harder to guess than the 6-number one, let's find how many options there are for each type.
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Letters in the Alphabet: & 26
Numbers from -9: & 10
If an event A has n possible outcomes and an event B has m possible outcomes, then the total number of different outcomes for A and B combined is n * m.
The product of the number of outcomes of each event gives us the total number of outcomes of the compound event. For the 4-letter password, we have 26 possible outcomes for each event. For the 6-number password, we have 10 possible outcomes for each event. Let's use the Fundamental Counting Principle to find the total number of outcomes for each password.
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4-letter password: && 6-number password: [0.8em]
26 * 26 && 10 * 10 * 10 * 26 * 26_(4events) && * 10* 10 * 10_(6events) [1.6em]
= 456 976 && = 1 000 000
Since 456 976 is less than 1 000 000, the password with the numbers is less likely to be guessed.
