Question

perform the indicated calculation.
₅₁p₂

₅₁p₂ = \square (type a whole number.)

Explanation:

Step1: Recall Permutation Formula

The formula for permutations is \( _nP_r=\frac{n!}{(n - r)!} \), where \( n = 51 \) and \( r=2 \).

Step2: Substitute Values into Formula

Substitute \( n = 51 \) and \( r = 2 \) into the formula: \( _{51}P_2=\frac{51!}{(51 - 2)!}=\frac{51!}{49!} \).

Step3: Simplify Factorials

Since \( n!=n\times(n - 1)\times\cdots\times1 \), we can write \( 51!=51\times50\times49! \). So, \( \frac{51!}{49!}=\frac{51\times50\times49!}{49!} \).

Step4: Cancel Out Common Terms

The \( 49! \) terms in the numerator and denominator cancel out, leaving \( 51\times50 \).

Step5: Calculate the Product

Calculate \( 51\times50 = 2550 \).

Answer:

2550