The Learning Questions:

(1) Anthony is choosing a toothbrush and a sponge. There are 16 different toothbrushes and some sponges. Anthony says, “There are 196 different ways to choose a toothbrush and a sponge”

Could Anthony be correct?

Show your working out.

(2) Three people A, B and C, enter a race.

**a.** Write down the different orders in which they can finish first, second and third.

**b.** Reasoning-Harry says that there are 3 possible winners, but then only 2 possibilities for second place and only one person left third place.

Is Harry correct? Explain your answer.

**c.** How many different ways can people finish in

**i** a 4-person race

**ii** a 6-person race

**iii** a 10 person race?

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