Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

Find the number of permutations of n distinct things taken r together, in which 3 parritcular things must occur together.

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.

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

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

The number of permutations of n different things taken r at a time in which 4 particular things never occur is -

Show that the numbers of permutations of n different things taken all at a time in which m particular things are never together is (n-m)!(n-m+1)! .

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 n things, taken r at a time, in which 3 particular things : (i) always occur (ii) will never occur.