Solve 30/frac{20*19*18*17*16{5*4*3*2*1}}

$$\frac{ 30 }{ \frac{ 20 \times 19 \times 18 \times 17 \times 16 }{ 5 \times 4 \times 3 \times 2 \times 1 } }$$

Evaluate

$$\frac{5}{2584}\approx 0.001934985$$

Solution Steps

Divide 30 by \frac{20\times 19\times 18\times 17\times 16}{5\times 4\times 3\times 2\times 1} by multiplying 30 by the reciprocal of \frac{20\times 19\times 18\times 17\times 16}{5\times 4\times 3\times 2\times 1}.

$$\frac{30\times 5\times 4\times 3\times 2\times 1}{20\times 19\times 18\times 17\times 16}$$

Cancel out 2\times 2\times 2\times 3\times 3\times 10 in both numerator and denominator.

$$\frac{5}{8\times 17\times 19}$$

Multiply 8 and 17 to get 136.

$$\frac{5}{136\times 19}$$

Multiply 136 and 19 to get 2584.

$$\frac{5}{2584}$$

Factor

$$\frac{5}{2 ^ {3} \cdot 17 \cdot 19} = 0.001934984520123839$$