91Ó°ÊÓ

You have forgotten the number sequence to your lock. You know that the correct code is made up of three numbers (right-left-right). The numbers can be from 0 to 39 and repetitions are allowed. If you can test one number sequence every 15 s, how long will it take to test all possible number sequences? Express your answer in hours.

Jodi is parking seven different types of vehicles side by side facing the display window at the dealership where she works. a) In how many ways can she park the vehicles? b) In how many ways can she park them so that the pickup truck is next to the hybrid car? c) In how many ways can she park them so that the convertible is not next to the subcompact?

a) Determine the middle term in the expansion of \(\left(a-3 b^{3}\right)^{8}\). b) Determine the term containing \(x^{11}\) in the expansion of \(\left(x^{2}-\frac{1}{x}\right)^{10}\).

How many integers from 3000 to 8999 inclusive, contain no 7s?

One term in the expansion of \((2 x-m)^{7}\) is \(-15120 x^{4} y^{3} .\) Determine \(m\).

Postal codes in Canada consist of three letters and three digits. Letters and digits alternate, as in the code R7B 5K1. a) How many different postal codes are possible with this format? b) Do you think Canada will run out of postal codes? Why or why not?

How many odd numbers of at most three digits can be formed using the digits \(0,1,2,3,4,\) and 5 without repetitions?

How many integers between 1 and 1000 do not contain repeated digits?

You have two colours of paint. In how many different ways can you paint the faces of a cube if each face is painted? Painted cubes are considered to be the same if you can rotate one cube so that it matches the other one exactly.

If \(100 !\) is evaluated, how many zeros are at the end of the number? Explain how you know.