Solve p(3)=51/(53)!3!

$$p ( 3 ) = \frac { 51 } { ( 53 ) ! 3 ! }$$

Evaluate

$$\frac{1}{502927445183532419329178088634047017610628680984331026432000000000000}\approx 1.98835838 \cdot 10^{-69}$$

Solution Steps

The factorial of 53 is 4274883284060025564298013753389399649690343788366813724672000000000000.

$$\frac{51}{4274883284060025564298013753389399649690343788366813724672000000000000\times 3!}$$

The factorial of 3 is 6.

$$\frac{51}{4274883284060025564298013753389399649690343788366813724672000000000000\times 6}$$

Multiply 4274883284060025564298013753389399649690343788366813724672000000000000 and 6 to get 25649299704360153385788082520336397898142062730200882348032000000000000.

$$\frac{51}{25649299704360153385788082520336397898142062730200882348032000000000000}$$

Reduce the fraction \frac{51}{25649299704360153385788082520336397898142062730200882348032000000000000} to lowest terms by extracting and canceling out 51.

$$\frac{1}{502927445183532419329178088634047017610628680984331026432000000000000}$$

Factor

$$\frac{1}{2 ^ {50} \cdot 3 ^ {23} \cdot 5 ^ {12} \cdot 7 ^ {8} \cdot 11 ^ {4} \cdot 13 ^ {4} \cdot 17 ^ {2} \cdot 19 ^ {2} \cdot 23 ^ {2} \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \cdot 47 \cdot 53} = 1.9883583796765594 \times 10^{-69}$$