Problem:
For any real number a and positive integer k, define
(ka)=k(k−1)(k−2)⋯(2)(1)a(a−1)(a−2)⋯(a−(k−1))
What is
(100−21)÷(10021)?
Answer Choices:
A. −199
B. −197
C. −1
D. 197
E. 199
Solution:
The answer is
100!(−21)(−23)⋯(−21−98)(−21−99)÷100!(21)(−21)(−23)⋯(21−99)=21(−21−99)=−199