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

Answer:

1. 15

2. 75

Step-by-step 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