At Dora's donut shop, dora makes 15 different varieties of donuts. Seven of these varieties are filled with jelly or cream. Officer sweetooth was sent to dora's shop to choose a dozen donuts, all different, with six filled and six unfilled. How many different assortments might he choose?
7 filled
8 unfilled
Choose 6 of each. So,
C(7,6) * C(8,6) = ?
20
196
196
To find the number of different assortments Officer Sweetooth can choose, we need to consider the following:
1. Choosing 6 filled donuts: Since there are seven filled varieties available, he can choose 6 donuts out of the 7 options in C(7, 6) different ways. (C(n, r) represents "n choose r" or the number of combinations of choosing r items out of a set of n items).
2. Choosing 6 unfilled donuts: Out of the 8 remaining donut varieties (15 total minus 7 filled varieties), he can choose 6 donuts out of the 8 options in C(8, 6) different ways.
To find the total number of different assortments, we need to multiply the number of possibilities for choosing filled donuts by the number of possibilities for choosing unfilled donuts:
C(7, 6) * C(8, 6) = 7 * 28 = 196
Therefore, Officer Sweetooth might have 196 different assortments to choose from.