There are arrangements in closed loops also, called as circular arrangements. Suppose n persons (a1, a2, a3… an) are to be arranged around a circular table. The total


When the positions are numbered, circular arrangement is treated as a linear arrangement.

In a linear arrangement, it does not make difference whether the positions are numbered or not.

Illustration 1:

Consider 23 different coloured beads in a necklace. In how many ways can the beads be placed in the necklace so that 3 specific beads always remain together?


By theory, let us consider 3 beads as one. Hence we have, in effect, 21 beads,   ‘n’ = 21. The number of arrangements = (n-1)! = 20!

Also, the number of ways in which 3 beads can be arranged between themselves is 3! = 3 x 2 x 1 = 6.

Thus the total number of arrangements = (1/2). 20! 3!

Illustration 2:

In how many ways 10 boys and 5 girls can sit around a circular table so that no two girls sit together.

« Click Here for Previous Topic Click Here for Next Topic »

Click Here for Class VII Maths All Topics Notes

You wish to report grammatical or factual errors within our online articles, you can let us know using the article feedback form.