Probability question

Question

A code consists of six digits chosen at random from 0 to 9.

the code can begin with a zero and digits can be repeated

how many codes will end with 0 ?

how many will contain the digits 2018 together and in this order?

Answer 1

Codes ending in 0

First 5 digits have 10⁵ possibilities (10 x 10 x 10 x 10 x 10) as 10 possibilities for each digit

Last digit is fixed

So 10⁵ codes ending in 0

For the second.

There are 3 ways we can place the 2018

2018..

.2018.

..2018

For each way there are 10² ways we can choose the other 2 digits

So number of ways = 3 x 10² = 300