Question:
Evaluate:
${ }^{10} \mathrm{P}_{4}$
Solution:
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 .
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