CBSE Class 7 Maths Notes: Permutation and Combination – Circular Permutations
Remarks:
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?
Solution:
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.
No comments:
Post a Comment