Solve 7!*8C_{4}

$$7 ! \times 8 C _ { 4 }$$

Evaluate

$$40320C_{4}$$

Solution Steps

The factorial of 7 is 5040.

$$5040\times 8C_{4}$$

Multiply 5040 and 8 to get 40320.

$$40320C_{4}$$

Differentiate w.r.t. C_4

$$40320$$

Steps Using Definition of a Derivative

The factorial of 7 is 5040.

$$\frac{\mathrm{d}}{\mathrm{d}C_{4}}(5040\times 8C_{4})$$

Multiply 5040 and 8 to get 40320.

$$\frac{\mathrm{d}}{\mathrm{d}C_{4}}(40320C_{4})$$

The derivative of ax^{n} is nax^{n-1}.

$$40320C_{4}^{1-1}$$

Subtract 1 from 1.

$$40320C_{4}^{0}$$

For any term t except 0, t^{0}=1.

$$40320\times 1$$

For any term t, t\times 1=t and 1t=t.

$$40320$$