Answer:
1680
Step-by-step explanation:
nPr = n!/(n-r)!
Therefore;
8P4 = 8!/(8-4)!
we get;
= 8!/4!
= (8×7×6×5×4×3×2×1)/(4×3×2×1)
= 40,320/ 24
= 1680
The expression is an illustration of factorials and permutations.
The value of [tex]\mathbf{^8P_4}[/tex] is 1680
The expression is given as:
[tex]\mathbf{^8P_4}[/tex]
Permutation is calculated as:
[tex]\mathbf{^nP_r = \frac{n!}{(n - r)!}}[/tex]
So, we have:
[tex]\mathbf{^8P_4 = \frac{8!}{(8 - 4)!}}[/tex]
Simplify
[tex]\mathbf{^8P_4 = \frac{8!}{4!}}[/tex]
Expand
[tex]\mathbf{^8P_4 = \frac{8 \times 7 \times 6 \times 5 \times 4! }{4!}}[/tex]
[tex]\mathbf{^8P_4 = 8 \times 7 \times 6 \times 5 }[/tex]
[tex]\mathbf{^8P_4 = 1680}[/tex]
Hence, the value of [tex]\mathbf{^8P_4}[/tex] is 1680
Read more about permutation and factorials at:
https://brainly.com/question/1216161
