Find the number of permutations of 10 objects, taken 4 at a time.

To find: the number of permutations of 10 objects, taken 4 at a time. 

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,

${ }_{n P_{r}}=\frac{n !}{(n-r) !}$

${ }_{10 p_{4}}=\frac{10 !}{6 !}$

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

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

Hence, the number of permutations of 10 objects, taken 4 at a time is 5040.