Suppose you flip four fair coins.

(a) Make a list of all the possible outcomes, as in below Table.

(b) Make a list of all the different “macrostates” and their probabilities.

(c) Compute the multiplicity of each macrostate using the combinatorial formula 2.6, and check that these results agree with what you got by brute-force counting.

TABLE: A list of all possible “microstates” of a set of three coins (where H is for heads and T is for tails).

Penny |
Nickel |
Dime |

H |
H |
H |

H |
H |
T |

H |
T |
H |

T |
H |
H |

H |
T |
T |

T |
H |
T |

T |
T |
H |

T |
T |
T |

Step 1 of 5</p>

(a) Make a list of all the possible outcomes, as in below Table.

All the possible outcomes (microstates) for the four coils is shown in below table.

Coin 1 |
Coin 2 |
Coin 3 |
Coin 4 |

H |
H |
H |
H |

H |
H |
H |
T |

H |
H |
T |
H |

H |
H |
T |
T |

H |
T |
H |
H |

H |
T |
H |
T |

H |
T |
T |
H |

H |
T |
T |
T |

T |
H |
H |
H |

T |
H |
H |
T |

T |
H |
T |
H |

T |
H |
T |
T |

T |
T |
H |
H |

T |
T |
H |
T |

T |
T |
T |
H |

T |
T |
T |
T |

For head= H and Tail = T, hence the total number of microstates =16=.