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