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?
10^3 for digits
(26-5)for first letter
26 for second letter
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
To find the number of different passwords that are possible, we need to consider each position in the password individually.
First position: Since the first digit must be the number 3, there is only one possibility.
Second position: Since repetition is allowed, any digit from 0 to 9 can be chosen. So, there are 10 possibilities.
Third and Fourth positions: Again, any digit from 0 to 9 can be chosen, so there are 10 possibilities for each position. Since repetition is allowed, we multiply the number of possibilities for each position together to get the total possibilities for these two positions. Therefore, there are 10 * 10 = 100 possibilities.
Fifth and Sixth positions: For the fifth position, any letter of the alphabet can be chosen. Since there are 26 letters in the English alphabet, there are 26 possibilities. Similarly, for the sixth position, there are 26 possibilities.
To find the total number of different passwords, we multiply the number of possibilities for each position together: 1 * 10 * 10 * 26 * 26 = 67,600.
Therefore, there are 67,600 different passwords that are possible based on the given conditions.