# Circular Permutations

**(i) Arrangements round a circular table****Arrangements of beads or flowers (all different) around a circular necklace or garland:**

**Conditional Permutations**

- Number of permutations of n things taking r at a time, in which a particular thing always occurs =.
- Number of permutations of n things taking r at a time, in which a particular thing never occurs = .
- Number of permutations of n different things taking all at a time, in which m specified things always come together =.
- Number of permutations of n different things taking all at a time, in which m specified things never comes together =
- The number of permutations of 'n' things taken all at a time, when 'p' are alike of one kind, 'q' are alike of second, 'r' alike of third, and so on.
- The number of permutations of 'n' different things, taking 'r' at a time, when each thing can be repeated 'r' times = n
^{r}