Question

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?

Answer 1

1. 15

2. 75

Explanation:

The possible outcomes are an apple (A), orange (O), lemon (L), banana (B), melon (M), and a joker (J), 6 outcomes in total.

1. You could win with 2 jokers in

`5+5+5=15` different ways.

You can list all these ways:

JJA JAJ AJJ

JJO JOJ OJJ

JJL JLJ LJJ

JJB JBJ BJJ

JJM JMJ MJJ

2. You could win with 1 joker in

`5\cdot 5+5\cdot 5+5\cdot 5=75`different ways

You can list all these ways:

JAA JAO JAL JAB JAM

JOA JOO JOL JOB JOM

JLA JLO JLL JLB JLM

JBA JBO JBL JBB JBM

JMA JMO JML JMB JMM

AJA AJO AJL AJB AJM

OJA OJO OJL OJB OJM

LJA LJO LJL LJB LJM

BJA BJO BJL BJB BJM

MJA MJO MJL MJB MJM

AAJ AOJ ALJ ABJ AMJ

OAJ OOJ OLJ OBJ OMJ

LAJ LOJ LLJ LBJ LMJ

BAJ BOJ BLJ BBJ BMJ

MAJ MOJ MLJ MBJ MMJ