Answer:
Option (c) is correct.
\(^5P_3\times^6C_4\) is 900
Step-by-step explanation:
Given :Expression \(^5P_3\times^6C_4\)
We have to find the value of given expression \(^5P_3\times^6C_4\)
Consider the given expression \(^5P_3\times^6C_4\)
The possibility of choosing an ordered set of r object from n object is given by
\(nPr=\frac{n!}{\left(n-r\right)!}\)
and The number of subset of r elements from n elements \(nCr=\frac{n!}{r!\left(n-r\right)!}\)
Thus, \(^5P_3=\frac{5!}{\left(5-3\right)!}==\frac{5!}{2!}=5\cdot \:4\cdot \:3=60\)
and \(^6C_4=\frac{6!}{4!\left(6-4\right)!}==\frac{6!}{4!\cdot \:2!}==\frac{6\cdot \:5}{2!}=15\)
Thus, \(^5P_3\times^6C_4=60\times 15=900\)
Thus, \(^5P_3\times^6C_4\) is 900
