Question

1. find the value of $^7p_1$. $^7p_1 = $ enter your next step here

Explanation:

Step1: Recall permutation formula

The formula for permutations is \( _nP_r=\frac{n!}{(n - r)!} \). For \( _7P_1 \), \( n = 7 \) and \( r = 1 \).

Step2: Substitute values into formula

Substitute \( n = 7 \) and \( r = 1 \) into the formula: \( _7P_1=\frac{7!}{(7 - 1)!}=\frac{7!}{6!} \).

Step3: Simplify factorials

Since \( n!=n\times(n - 1)\times\cdots\times1 \), \( 7!=7\times6! \). So \( \frac{7!}{6!}=\frac{7\times6!}{6!} \).

Step4: Cancel out common terms

The \( 6! \) terms in the numerator and denominator cancel out, leaving \( 7 \).

Answer:

\( 7 \)