Question

use a calculator to evaluate the expression.

(_{19}p_8)

(_{19}p_8 = square)
(use scientific notation. use the multiplication symbol in the math palette as neede

Explanation:

Step1: Recall the permutation formula

The formula for permutations is \( _nP_r=\frac{n!}{(n - r)!} \), where \( n = 19 \) and \( r=8 \). So \( _{19}P_8=\frac{19!}{(19 - 8)!}=\frac{19!}{11!} \).

Step2: Simplify the factorial expression

Since \( n!=n\times(n - 1)\times\cdots\times1 \), we can write \( 19! = 19\times18\times17\times16\times15\times14\times13\times12\times11! \). Then \( \frac{19!}{11!}=19\times18\times17\times16\times15\times14\times13\times12 \).

Step3: Calculate the product

Using a calculator to multiply these numbers: \( 19\times18 = 342 \), \( 342\times17=5814 \), \( 5814\times16 = 93024 \), \( 93024\times15=1395360 \), \( 1395360\times14 = 19535040 \), \( 19535040\times13=253955520 \), \( 253955520\times12 = 3047466240 \). In scientific notation, this is \( 3.04746624\times 10^{9} \).

Answer:

\( 3.04746624\times 10^{9} \)