A slot machine has 3 slots. For each slot, the possible outcomes are an apple, orange, lemon, banana, melon, and a joker. When the player puts a coin in the machine, a wheel spins in each of the three slots and stops randomly on one of the possible outcomes. There are different ways to win for each coin played--All 3 jokers are visible, any 3 of a kind that isn't a joker, any 2 jokers, or any 1 joker.
1. How many ways could you win with 2 jokers?
2. How many ways could you win with 1 joker?
+29 IF THE ORDER OF THE JOKERS AND FRUIT DOES NOT MATTER:
1. All you have to do is choose the fruit to appear, so there are \(5\) possible ways to win.
2. You have to choose the first fruit (five ways) and choose the second fruit (five ways) so there are \(25\) possible ways to win.
IF THE ORDER OF THE JOKERS AND FRUIT DOES MATTER:
1. Choose the slot that will not have a joker (three ways) and the fruit to appear in it (five ways), so there are \(15\) possible ways to win.
2. Two cases.
Case 1: Joker and two different fruits.
Choose the slot that will have a joker (three ways) and the slot that will have one of the fruits (two ways) and then that fruit (five ways) and then the second fruit (four ways), so there are \(120\) possible ways to win.
Case 2: Joker and two of the same fruit.
Choose the slot that will have a joker (three ways) and then the type of fruit (five ways), so there are \(15\) possible ways to win.
ANSWER: \(135\) ways to win.
I hope this is helpful,
Catarina
