Question

evaluate the expression. (example 2)

1. ( _7p_3 )

Explanation:

Step1: Recall Permutation Formula

The formula for permutations is \( _nP_r=\frac{n!}{(n - r)!} \), where \( n = 7 \) and \( r=3 \).

Step2: Substitute Values

Substitute \( n = 7 \) and \( r = 3 \) into the formula: \( _7P_3=\frac{7!}{(7 - 3)!}=\frac{7!}{4!} \).

Step3: Expand Factorials

We know that \( n!=n\times(n - 1)\times\cdots\times1 \), so \( 7! = 7\times6\times5\times4! \) and \( 4! = 4! \). Then \( \frac{7!}{4!}=\frac{7\times6\times5\times4!}{4!} \).

Step4: Simplify

Cancel out \( 4! \) from numerator and denominator: \( 7\times6\times5 = 210 \).

Answer:

210