Answer:
Option B is correct.
Step-by-step explanation:
We have been given an expression:
[tex]^{12}P_5[/tex]
Above expression is of permutation we have a formula to solve the permutation which is:
[tex]^n{P}_r=\frac{n!}{(n-r)!}[/tex]
Here, n=12 and r=5
On substituting the values in the formula we get:
[tex]^12{P}_5=\frac{12!}{(12-5)!}[/tex] (1)
And also: [tex]n!=n(n-1)(n-2)....1[/tex]
Equation 1 becomes after first step of simplification:
[tex]\frac{12!]{7!}[/tex]
[tex]\frac{12\cdot11\cdot10\cdot9\cdot8\cdot7!}{7!}[/tex]
Common term from numerator and denominator which is 7! will get cancelled we get:
[tex]12\cdot11\cdot10\cdot9\cdot8[/tex]
After simplification we get:
95040
Therefore, Option B is correct
