Question

A lock has a code of 5 numbers from 1 to 15. If no numbers in the code are allowed to repeat, how many different codes could be made?​

Answer 1

There are 116,280 different codes that can be made with 4 numbers between 1 and 20 without repeating any number.

Explanation:

What are permutation and combination?

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,

To find the number of different codes that can be made with 4 numbers between 1 and 20 without repeating any number, we can use the permutation formula, nPr = n! / (n-r)! where n is the total number of items and r is the number of items we want to choose.

In this case, we have n = 20 (the total number of numbers we can choose from) and r = 4 (the number of numbers we need to choose).

So, the number of different codes that can be made is:

20P4 = 20! / (20-4)! = 20! / 16! = 20 × 19 × 18 × 17 = 116,280

Therefore, there are 116,280 different codes that can be made with 4 numbers between 1 and 20 without repeating any number.