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

(1) Code that ends with zero looks like this:

XXXXX0

Since each an X has a possibility of 10 digits and the last digit has only 1 possibility.

(10)(10)(10)(10)(10)(1)

=(10⁵)(1)

=100,000 codes

(2)These are the only possible formats:

2018XX, X2018X, XX2018

Remember, each X has 10 possible digits.

(10)(10) + (10)(10) + (10)(10) = 300 codes