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Enter the mathematical formula directly and click the "Next" button to get the calculation answer.
It supports mathematical functions (including trigonometric functions).
Current location：Mathematical operation > History of Mathematical Computation > Answer
Overview: 1 questions will be solved this time.Among them
☆1 arithmetic calculations
[1/1 Formula]
Work: Calculate the value of equation !(8)-C(7,1)*!(7)+C(7,2)*!(6)-C(7,3)*!(5)+C(7,4)*!(4)-C(7,5)*!(3)+C(7,6)*!(2)-C(7,7)*1 .
Question type: Mathematical calculation
Solution:
!(8)-C(7,1)*!(7)+C(7,2)*!(6)-C(7,3)*!(5)+C(7,4)*!(4)-C(7,5)*!(3)+C(7,6)*!(2)-C(7,7)*1
=40320-C(7,1)*!(7)+C(7,2)*!(6)-C(7,3)*!(5)+C(7,4)*!(4)-C(7,5)*!(3)+C(7,6)*!(2)-C(7,7)*1
=40320-7*!(7)+C(7,2)*!(6)-C(7,3)*!(5)+C(7,4)*!(4)-C(7,5)*!(3)+C(7,6)*!(2)-C(7,7)*1
=40320-7*5040+C(7,2)*!(6)-C(7,3)*!(5)+C(7,4)*!(4)-C(7,5)*!(3)+C(7,6)*!(2)-C(7,7)*1
=40320-7*5040+21*!(6)-C(7,3)*!(5)+C(7,4)*!(4)-C(7,5)*!(3)+C(7,6)*!(2)-C(7,7)*1
=40320-7*5040+21*720-C(7,3)*!(5)+C(7,4)*!(4)-C(7,5)*!(3)+C(7,6)*!(2)-C(7,7)*1
=40320-7*5040+21*720-35*!(5)+C(7,4)*!(4)-C(7,5)*!(3)+C(7,6)*!(2)-C(7,7)*1
=40320-7*5040+21*720-35*120+C(7,4)*!(4)-C(7,5)*!(3)+C(7,6)*!(2)-C(7,7)*1
=40320-7*5040+21*720-35*120+35*!(4)-C(7,5)*!(3)+C(7,6)*!(2)-C(7,7)*1
=40320-7*5040+21*720-35*120+35*24-C(7,5)*!(3)+C(7,6)*!(2)-C(7,7)*1
=40320-7*5040+21*720-35*120+35*24-21*!(3)+C(7,6)*!(2)-C(7,7)*1
=40320-7*5040+21*720-35*120+35*24-21*6+C(7,6)*!(2)-C(7,7)*1
=40320-7*5040+21*720-35*120+35*24-21*6+7*!(2)-C(7,7)*1
=40320-7*5040+21*720-35*120+35*24-21*6+7*2-C(7,7)*1
=40320-7*5040+21*720-35*120+35*24-21*6+7*2-1*1
=40320-35280+21*720-35*120+35*24-21*6+7*2-1*1
=40320-35280+15120-35*120+35*24-21*6+7*2-1*1
=40320-35280+15120-4200+35*24-21*6+7*2-1*1
=40320-35280+15120-4200+840-21*6+7*2-1*1
=40320-35280+15120-4200+840-126+7*2-1*1
=40320-35280+15120-4200+840-126+14-1*1
=40320-35280+15120-4200+840-126+14-1
=5040+15120-4200+840-126+14-1
=20160-4200+840-126+14-1
=15960+840-126+14-1
=16800-126+14-1
=16674+14-1
=16688-1
=16687
Answer:!(8)-C(7,1)*!(7)+C(7,2)*!(6)-C(7,3)*!(5)+C(7,4)*!(4)-C(7,5)*!(3)+C(7,6)*!(2)-C(7,7)*1=16687