Your sweetie loves chocolate. You bought your sweetie some chocolate: an assortment of 24 chocolates with six each of four flavours. “Oh, honey, you shouldn’t have.” Why not? Unfortunately, chocolate causes your sweetie to gain weight per the following table:

Flavour | Weight Gain in Grams per Chocolate Eaten |

Nougat | 100 |

Honey | 200 |

Solid Chocolate | 900 |

Anthrax Ripple | -200 |

Your sweetie selects four chocolates at random and eats them.

What is the probability of each of the following scenarios occurring (assuming no other factors that affect weight)?

Scenario 1: Your sweetie gains two or more kilograms.

Scenario 2: Your sweetie’s weight does not change.

Scenario 3: Your sweetie loses weight.

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. **The deadline is Wednesday, March 1, 2017 at noon Pacific Time.** I will post the answer shortly after.