Dainty Donuts is preparing a Christmas promotion, offering a standard discount on their 12-donut boxes. Anticipating the season, Dainty has also developed 8 new Christmas donuts. The Christmas discount applies to donut boxes containing 4 Christmas donuts and 8 donuts from a selection of the 10 most popular donuts for the year:

Chocolate Frosted

Sugar

Bavarian Kreme

Glazed

Powdered

Boston Kreme

Blueberry Filled

Double Chocolate

Strawberry Filled

Red Velvet

a. How many donut box combinations are possible? Assume that the Christmas discount applies only to 12-donut boxes containing only one item of any particular donut type.

b. Angelo da Silva, a donut connoisseur, does not particularly care about the upcoming Dainty Donuts Christmas promotion. He doesn't intend to try any of the new Christmas donuts. What he does care about is that any 12-donut box he purchases this coming Christmas should contain at least one set of three of any of his favorite donuts, which include:

Bavarian Kreme

Blueberry Filled

Double Chocolate

Da Silva's 12-donut box contains any of his favorite donuts in sets of three, and any remaining donut types in singles.