Your password for a given website is made up of three letters followed by
four numbers. Find the number of possible passwords if there are no
restrictions on what three letters and what four numbers can be used.
Pls check if my answer is correct
26C3*10C4
=26!/(26-3)!3! . 10!/(10-4)!4!
= 26*25*24*23!/23!*6 . 10*9*8*7*6!/6!*4*3*2*1
=15600/6 * 5040/24
=2600*210
see below
To find the number of possible passwords, you correctly used the concept of combinations. However, there is a small mistake in calculating the final value.
The number of ways to choose 3 letters from a set of 26 letters can be calculated as 26C3, which is given by:
26C3 = 26! / (3! * (26-3)!)
= 26! / (3! * 23!)
= (26 * 25 * 24) / (3 * 2 * 1)
= 26 * 25 * 24 / 6
= 2600
Similarly, the number of ways to choose 4 numbers from a set of 10 numbers can be calculated as 10C4, which is given by:
10C4 = 10! / (4! * (10-4)!)
= 10! / (4! * 6!)
= (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)
= 10 * 9 * 8 * 7 / 24
= 210
Now, to calculate the total number of possible passwords, you need to multiply the number of ways to choose the letters and the number of ways to choose the numbers:
Total number of passwords = 2600 * 210
= 546,000
So the correct answer is 546,000 possible passwords.