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

Find the number of permutations of 7 objects, taken 3 at a time.

Find the number of permutations of 12 things, taken 6 at a time, in which 3 particular things are : included .

Find the number of permutations of 12 things, taken 6 at a time, in which 3 particular things are : excluded .

Find the number of permutations of 20 things taken 5 at a time so that one particular thing will always occur

Find the number of permutations of 20 things taken 5 at a time so that one particular thing will never occur.

Find the number of permutations of 8 things, taken 3 at a time, in which 2 particular things are always : included .

Find the number of permutations of 8 things, taken 3 at a time, in which 2 particular things are always : excluded .

Find the number of permutations of n things, taken r at a time, in which 3 particular things : always occur.

Find the number of permutations of n things, taken r at a time, in which 3 particular things : will never occur.