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Evaluate. $\newline$ $_4P_2 = \_\_\_\_\_$

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Permutation and combination notation

Full solution

Q. Evaluate.

\newline

_4P_2 = \_\_\_\_\_

Identify Permutation Formula: Identify the permutation formula for $4P2$ . $\newline$ Substitute $4$ for $n$ and $2$ for $r$ in the formula. $\newline$ $4P2 = \frac{n!}{(n - r)!}$ $\newline$ $4P2 = \frac{4!}{(4 - 2)!}$
Substitute Values: Calculate the factorial values and simplify the expression. $\newline$ $4P2 = \frac{4!}{(4 - 2)!}$ $\newline$ $4P2 = \frac{4!}{2!}$ $\newline$ $4P2 = \frac{(4 \times 3 \times 2 \times 1)}{(2 \times 1)}$
Calculate Factorials: Cancel out the common terms in the numerator and the denominator. $\newline$ $4P2 = \frac{4 \times 3 \times 2 \times 1}{2 \times 1}$ $\newline$ $4P2 = \frac{4 \times 3}{1}$ $\newline$ $4P2 = 12$

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