# Lesson Worksheet: Counting Outcomes with Restrictions Mathematics

In this worksheet, we will practice finding the number of outcomes in a probability problem with a condition.

Q1:

In how many ways can an odd number of 6 digits be formed using the digits if no digits are to be repeated?

Q2:

How many four-digit numbers, with no repeated digits, can be formed using the elements of the set ?

Q3:

Find the number of ways to form a 2-digit number, with no repeated digits, given 4 diﬀerent digits to choose from.

Q4:

Phone numbers on a particular network are twelve-digit long, where the first three digits are always 072. Calculate the total number of different phone numbers which the network can use.

Q5:

How many three-digit numbers that are less than 900 and that have no repeated digits can be formed using the elements of the set ?

Q6:

In how many ways can a three-digit number, starting with an even digit and containing no repeated digits, be formed from the numbers ?

Q7:

Five children need to sit at the back of a coach. There are five seats next to one another. However, Matthew and Benjamin do not want to sit next to each other. How many ways can the children sit in the five seats so that Matthew and Benjamin are not sitting next to each other?

Q8:

Mia and Daniel are planning their wedding. They are working on the seating plan for the head table at the reception. Their head table is a straight table with 8 seats down one side; it needs to seat the bride and groom, the bride’s parents, the groom’s parents, the best man, and the maid of honor. Given that all couples need to sit next to each other and that the best man and maid of honor are not a couple, how many different options are there for seating everyone at the head table?

Q9:

David’s password must be five characters long. He can use the digits 0 to 9, and cannot use the same digit more than once. How many different passwords could David create?

Q10:

A building has 5 doors which are numbered as . Determine the number of ways a person can enter, and then leave the building, if they cannot use the same door twice.

This lesson includes 25 additional questions and 180 additional question variations for subscribers.