Problem: What is 10!−7!⋅6!10!-7!\cdot 6!10!−7!⋅6! ?
Answer Choices:
A. −120-120−120
B. 000
C. 120120120
D. 600600600
E. 720720720
Solution:
Note that
10!−7!⋅6!=7!⋅(10⋅9⋅8−6!)=7!⋅(720−720)=(B)010!-7!\cdot 6!=7!\cdot(10 \cdot 9 \cdot 8-6!)=7!\cdot(720-720)=(\text{B})\boxed{0} 10!−7!⋅6!=7!⋅(10⋅9⋅8−6!)=7!⋅(720−720)=(B)0
The problems on this page are the property of the MAA's American Mathematics Competitions