Determine the number of combinations on a bicycle lock that has a 3-digit number combination with only 3 numbers where the numbers can be repeated to open the lock
To determine the number of combinations on a bicycle lock with a 3-digit combination using only 3 numbers where repetition is allowed, you can use the concept of permutations.
A permutation is an arrangement of items where the order matters. In this case, the order of the numbers in the combination matters. However, since repetition is allowed, it is more accurate to calculate the number of combinations rather than permutations.
To find the number of combinations, you can use the formula for combinations:
C(n, r) = n! / (r! * (n-r)!)
Where:
C(n, r) is the number of combinations
n is the total number of numbers to choose from
r is the number of items chosen at a time
! denotes the factorial operation
In this case, to find the number of combinations on the bicycle lock, we have:
n = 10 (since there are 10 digits to choose from: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
r = 3 (since we want a 3-digit combination)
Plugging these values into the formula, we get:
C(10, 3) = 10! / (3! * (10-3)!)
= 10! / (3! * 7!)
= (10 * 9 * 8) / (3 * 2 * 1)
= 720 / 6
= 120
Therefore, the number of combinations on the bicycle lock is 120.
looks like just
3x3x3 or 27 to me