Counting Combinations III

You have letters a, f, q, r and d. Make a code with any of these 3 letters. How many possible codes can be there? Use all the letters. (Use the multiplication method)

• 27

• 34

• 15

• 17

Answer explanation

It is because there are 5 letters, and you need to take 3 of them to make a code. Hence, multiply 5 by 3 which is 15. Thereby we can make 15 codes out of these letters.

From a list of 10 songs, you are asked to pick your 1st, 2nd, and 3rd favorite songs.

How many different combinations of choices are there?

Answer explanation

You have 10 choices for the 1st song, 9 choices for the 2nd song (because you can’t choose

the same song again), and 8 choices for the 3rd song [do you know why?] Because we cannot repeat the two songs which we have already chosen.) [We should do 10-2= 8.]

So, the total number of combinations is 10 x 9 x 8 = 720. 😊

A card game uses a special deck where each card has a number and a color.

The numbers range from 1 to 12. The colors are red, orange, yellow, green, and blue.

For example, there is a “5 blue” card. If the deck has one card with each of the possible

combinations of number and color, how many cards are there in the deck?

Answer explanation

Here there are 5 colours and 12 numbers hence we will multiply 12 by 5 which is 60.

The Class Council is selling T-shirts that come in 3 colors (yellow, blue, white) and

4 sizes (small, medium, large, extra large).

Using the multiplication principle, how many different kinds of T-shirts are available?

Write your answer and draw it in the space below.

• 34

• 35

• 32

• 12

Suppose you flip a coin 4 times. Each time, the coin is either heads (H) or tails (T).

An example of a sequence of 4 coin flips would be: HTTH.

Now, answer this question to figure out how many different coin flip sequences there are.

How many total possible outcomes are there for all the flips?

• 16

• 27

• 60

• 34

Answer this question based upon the coin flip one.

How many possible outcomes are there for the second flip?

• 44

• 4

• 5

• 23

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