Question

Please help!!!!!!!!!!!!!!!! 100pts,

Answer 1

QUESTION:

The code for a lock consists of 5 digits (0-9). The last number cannot be 0 or 1. How many different codes are possible.

ANSWER:

Since in this particular scenario, the order of the numbers matter, we can use the Permutation Formula:–

• P(n,r) = n!/(n−r)! where n is the number of numbers in the set and r is the subset.

Since there are 10 digits to choose from, we can assume that n = 10.

Similarly, since there are 5 numbers that need to be chosen out of the ten, we can assume that r = 5.

Now, plug these values into the formula and solve:

= 10!(10−5)!

= 10!5!

= 10⋅9⋅8⋅7⋅6

= 30240.