At the beginning of every period of British Literature, Mrs. Crabapple picks a random student to receive a crabapple as a gift, but really, as you might imagine, they are quite bitter and nasty. Given that there are 11 students in her class and her class meets four times a week, how many different sequences of crabapple recipients are possible in a week?
Since there is no mention that a student cannot be picked twice, there are 11 possible victims every time the class meets. Therefore, our answer is $11 \cdot 11 \cdot 11 \cdot 11 = 11^4 = \boxed{14,\!641}.$
14641
Level 5
Prealgebra
Problem: At the beginning of every period of British Literature, Mrs. Crabapple picks a random student to receive a crabapple as a gift, but really, as you might imagine, they are quite bitter and nasty. Given that there are 11 students in her class and her class meets four times a week, how many different sequences of crabapple recipients are possible in a week?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To determine the number of different sequences of crabapple recipients in a week, we need to consider the number of choices available for each day. There are 11 students in the class, and Mrs. Crabapple picks one student each day. Since the class meets four times a week, we have four days of selections.

For each day, Mrs. Crabapple has 11 independent choices (one for each student). The selections made on different days do not affect each other, meaning the choices are independent events. Therefore, we can use the multiplication principle of counting to find the total number of sequences.

The total number of sequences can be calculated as follows:

1. For Day 1, there are 11 choices.
2. For Day 2, there are again 11 choices.
3. For Day 3, there are 11 choices.
4. For Day 4, there are 11 choices.

To find the total number of sequences over the four days, we multiply the number of choices for each day:

Total sequences = 11 (Day 1) * 11 (Day 2) * 11 (Day 3) * 11 (Day 4)

This can be expressed mathematically as:

Total sequences = 11^4

Now, we calculate 11 raised to the power of 4:

11^4 = 11 * 11 * 11 * 11

Calculating step-by-step:

1. 11 * 11 = 121
2. 121 * 11 = 1331
3. 1331 * 11 = 14641

Thus, the total number of different sequences of crabapple recipients in a week is 14641.<|END_OF_LATENT|> The final answer is $14641$.