# List Outcomes Systematically

In this worksheet, students practise finding and using all the combinations for a given situation.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Probability

Curriculum subtopic:   Probability, Combined Events and Probability Diagrams

Difficulty level:

### QUESTION 1 of 10

Sometimes you get a question where there a loads of different options to choose from and it's difficult to see which option to choose.

If you get a question like this, you need to use a systematic listing stategy to write out all the combinations.

Example 1: A shop sells beef, plain and salt n vineger crisps and coke or fanta.

If you wanted to buy one bag of crisps and a drink, how many options do you have.

To solve this, we need to look at one of the options first and see how many of the other options you could have.

So: Beef Crisps could be bought with either Coke or Fanta           (B,C   B,F)

Next: Plain crisps could be bought with either Coke or Fanta        (P, C   P,F)

Lastly: Salt n Vinegar could be bought with Coke or Fanta           (S,C   S,F)

From this we can see that there are 6 different options.

The link with probability.

These questions are frequently paired with probability.

Example: A shop sells beef, plain and salt n vineger crisps and coke or fanta.

If someone randomly bought one bag of crisps and a drink, what is the probability they bought Beef Crisps and a fanta?

We know that there are 6 options in total and only one of these is the one we are looking for.

The probability will therefore be 1/6

Systematic listing is where you write out....

If I flip two coins at the same time, how many different outcomes could I have?

In a deli, I can choose to have either plain, italian, cheesy or rye bread for a sandwich

I can fill this with with either Ham, Cheese or Beef.

How many different sandwiches could I make?

7

12

In a deli, I can choose to have either plain, italian, cheesy or rye bread for a sandwich

I can fill this with with either Ham, Cheese or Beef.

What is the probability I get beef on rye bread?

Write your answer as a fraction of the form a/b

Match the situation to the number of combinations.

## Column B

5 options for A, 4 options for B
4
3 options for A, 6 options for B
36
2 options for A, 2 options for B
20
6 options for A, 6 options for B
18

I have three scrabble tile with A, B and C on them.

without looking, I pick one up and then another.

How many different ways could I do this?

I choose two vowels at random. How many different ways could I do this?

5

20

25

I choose two vowels at random. If I can't pick the same one twice, how many different ways could I do this?

5

20

25

I pick a number between 1 and 9, I then do this again.

How many different ways can I do this

I pick a number between 1 and 9, I then do this again.

What is the probability I have chosen the numbers 3 and 7?

Give your answers as a fraction in the form a/b

• Question 1

Systematic listing is where you write out....

EDDIE SAYS
We use systematic listing to write out all the things that could happen. We call this combinations of outcomes.
• Question 2

If I flip two coins at the same time, how many different outcomes could I have?

4
EDDIE SAYS
Think logically. If I get a head on one, I could get either a head or a tail on the other (HH, HT) If I get a tail on one, I could get a head or a tail on the other. (TH,TT)
• Question 3

In a deli, I can choose to have either plain, italian, cheesy or rye bread for a sandwich

I can fill this with with either Ham, Cheese or Beef.

How many different sandwiches could I make?

12
EDDIE SAYS
For each type of bread, I can have 3 different fillings. 4 lots of 3 is 12
• Question 4

In a deli, I can choose to have either plain, italian, cheesy or rye bread for a sandwich

I can fill this with with either Ham, Cheese or Beef.

What is the probability I get beef on rye bread?

Write your answer as a fraction of the form a/b

1/12
EDDIE SAYS
There are 12 different options, but only one of them describes what im looking for. This gives a probability of 1/12
• Question 5

Match the situation to the number of combinations.

## Column B

5 options for A, 4 options for B
20
3 options for A, 6 options for B
18
2 options for A, 2 options for B
4
6 options for A, 6 options for B
36
EDDIE SAYS
Let\'s look at one of these 5 options for A, 4 options for B For each of the 5 options for A, I have 4 for B so I can have 4 + 4 + 4 + 4 + 4 combinations in total . The quick trick to find out how many combinations I have is to multiply the amount of options together.
• Question 6

I have three scrabble tile with A, B and C on them.

without looking, I pick one up and then another.

How many different ways could I do this?

6
EDDIE SAYS
This is a bit different than the others. If I pick up one (A, B or C) then there are only 2 left for the second one. So my options are AB AC BA BC CA CB
• Question 7

I choose two vowels at random. How many different ways could I do this?

25
EDDIE SAYS
I have 5 options for each one, so I have 5 lots of 5 to choose from.
• Question 8

I choose two vowels at random. If I can't pick the same one twice, how many different ways could I do this?

20
EDDIE SAYS
I have 5 options for my first choice, but because I can\'t pick the same one twice, I only have 4 options for the other.
• Question 9

I pick a number between 1 and 9, I then do this again.

How many different ways can I do this

81
EDDIE SAYS
There are 9 options for the first number I pick and 9 for the second. This gives me 81 combinations
• Question 10

I pick a number between 1 and 9, I then do this again.

What is the probability I have chosen the numbers 3 and 7?

Give your answers as a fraction in the form a/b

2/81
EDDIE SAYS
There are 9 options for the first number I pick and 9 for the second. This gives me 81 combinations The questions doesn\'t say that the numbers have to be 3 then 7. They could also be 7 then 3. This gives me 2 options out of 81
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