If a school has lockers with
50 numbers on each combination
lock, how many possible
combinations using three
numbers are there.
how about 50*50*50?
Naturally, the sequential numbers in the combination cannot be too close together, because of the physical mechanisms of the lock, but in theory all sequences of three of the 50 numbers are possible.
450
its not 450
To find the number of possible combinations using three numbers on a combination lock with 50 numbers, we can use the concept of permutations.
Since we have 50 numbers on each dial and we need to choose 3 numbers, the formula to find the number of permutations is given by:
P(n, r) = n! / (n-r)!
Where "n" is the total number of options and "r" is the number of choices we need to make.
In this case, we have 50 options (numbers) and we need to choose 3 numbers. Plugging these values into the formula, we get:
P(50, 3) = 50! / (50-3)! = 50! / 47!
Now, let's calculate the value using this formula:
First, calculate the factorial of 50:
50! = 50 * 49 * 48 * 47! (cancelling out the 47! term in the denominator)
Simplifying this further:
50! = (50 * 49 * 48)
So, the number of possible combinations using three numbers on a combination lock with 50 numbers is:
(50 * 49 * 48) = 117,600 combinations.