Solve 7!/2!(7-2)!(0.4^2)(0.6^5)

$$\frac{ 7 ! }{ 2 ! (7-2) ! } ( { 0.4 }^{ 2 } )( { 0.6 }^{ 5 } )$$

Evaluate

$$0.2612736$$

Solution Steps

The factorial of 7 is 5040.

$$\frac{5040}{2!\left(7-2\right)!}\times 0.4^{2}\times 0.6^{5}$$

The factorial of 2 is 2.

$$\frac{5040}{2\left(7-2\right)!}\times 0.4^{2}\times 0.6^{5}$$

Subtract 2 from 7 to get 5.

$$\frac{5040}{2\times 5!}\times 0.4^{2}\times 0.6^{5}$$

The factorial of 5 is 120.

$$\frac{5040}{2\times 120}\times 0.4^{2}\times 0.6^{5}$$

Multiply 2 and 120 to get 240.

$$\frac{5040}{240}\times 0.4^{2}\times 0.6^{5}$$

Divide 5040 by 240 to get 21.

$$21\times 0.4^{2}\times 0.6^{5}$$

Calculate 0.4 to the power of 2 and get 0.16.

$$21\times 0.16\times 0.6^{5}$$

Multiply 21 and 0.16 to get 3.36.

$$3.36\times 0.6^{5}$$

Calculate 0.6 to the power of 5 and get 0.07776.

$$3.36\times 0.07776$$

Multiply 3.36 and 0.07776 to get 0.2612736.

$$0.2612736$$

Factor

$$\frac{7 \cdot 2 ^ {2} \cdot 3 ^ {6}}{5 ^ {7}} = 0.2612736$$