Question:
Evaluate:
${ }^{6} \mathrm{P}_{6}$
Solution:
To find: the value of ${ }^{6} \mathrm{P}_{6}$
Formula Used:
Total number of ways in which $n$ objects can be arranged in $r$ places (Such that no object is replaced) is given by,
${ }_{n P_{r}}=\frac{n !}{(n-r) !}$
Therefore,
${ }_{6} \mathrm{P}_{6}=\frac{6 !}{(6-6) !}$
${ }^{62} P_{3}=6 \times 5 \times 4 \times 3 \times 2 \times 1=720$
Thus, the value of ${ }^{6} \mathrm{P}_{6}$ is 720 .