A gate has a standard key pad with the digits 0 through 9. How many possible code combinations are there if the code is 3 digits long.
nine things arranged 3 at a time, order matters
that is "permutations"
n! / [ n-r] !
n = 9
r = 3
n-r = 6
so = 9*8*7*6*5*4*3*2*1 / 6*5*4*3*2*1
so = 9*8*7
Whoops sorry TEN things
You can fix it
10*9*8
Well, isn't that a pressing question! Let's do some math, shall we?
Since the keypad has 10 digits (0 through 9), and we want to crack a 3-digit code, we need to consider how many choices we have for each digit.
For the first digit, we have 10 options. Similarly, for the second digit, we still have 10 options. And for the third digit, you guessed it, we also have 10 options.
To find the total number of possible combinations, we multiply the number of choices together: 10 x 10 x 10 = 1000.
So, there are 1000 possible code combinations for a 3-digit code on that gate. Good luck cracking it... or finding the keys if you lost them!
To determine the number of possible code combinations, we need to calculate the total number of choices for each digit and then multiply them together.
Since the keypad has ten digits (0 through 9), there are 10 options for each digit of the code.
Since the code is three digits long, we need to multiply the number of choices for each digit together three times.
Therefore, the total number of possible code combinations can be calculated as:
10 choices for the first digit × 10 choices for the second digit × 10 choices for the third digit = 10^3 = 1,000
So, there are 1,000 possible code combinations if the code is three digits long.