Evaluate:

To find: the value of ${ }^{10} \mathrm{P}_{4}$

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,

${ }_{10 p_{4}}=\frac{10 !}{(10-4) !}$

${ }^{10} \mathrm{P}_{4}=10 \times 9 \times 8 \times 7$

${ }^{10} \mathrm{P}_{4}=5040$

Thus, the value of ${ }^{10} \mathrm{P}_{4}$ is 5040 .