Answer: The required value of the given expression is 720.
Step-by-step explanation: We are given to evaluate the following expression :
\(E=^6P_5.\)
We know that
the formula for the number of permutations of n different things taken r (r is less than or equal to n) at a time is given by
\(^nP_r=\dfrac{n!}{(n-r)!}.\)
Therefore, the given expression can be evaluated as follows :
\(E\\\\=^6P_5\\\\\\=\dfrac{6!}{(6-5)!}\\\\\\=\dfrac{6!}{1!}\\\\\\=\dfrac{6\times5\times4\times3\times2\times1}{1}\\\\=720.\)
Thus, the required value of the given expression is 720.
