Question

The code for a safe is a six-digit sequence, for example 013255. How many different (can repeat numbers) codes can you get? How many different codes (can repeat numbers) of even numbers are there?

Answer 1

1,000,000 codes

500,000 even

Explanation:

1.

There are 10 different options, 0 - 9, for every digit in the 6-digit sequence;

Since numbers can be repeated, it is very simple;

Imagine a tree diagram, there will 10 branches, since there are 10 options for any given digit, and there will 6 layers, since there are 6 digits in thr sequence;

Hence, the number of possible codes will be:

(10)⁶ = 1,000,000

The way this particular scenario works out is, every number between 0 and 999,999 is a possibility;

There are 1,000,000 numbers between 0 and 999,999 and hence this many possibilities;

This is another way of finding the number of codes.

2.

Consider 0 to 9, 0, 2, 4, 6 and 8 are even, and all others are odd;

There are 5 even in total and 5 odd;

Similarly between 0 and 99, 50 will be even and 50 will be odd;

Therefore between 0 and 999,999, 500,000 will be even and 500,000 will be odd;

Its ½ and ½.