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