Circular Permutation 1

At the table, 5 boys and 4 girls are to be seated on a round table. How many ways can this be done if

(i) there is no restrictions

(ii) there is no restrictions and the seats are numbered

(iii) 4 girls must sit together

(iv) 3 particular boys cannot sit together



(i) 40320

(9-1)! = 40320


(ii) 362880


(iii) 2880

(6-1)! x 4! = 2880

Note: (6-1)! is arranging the number of entities in a circle, not 6!


(iv) 14400

(6-1)! x 6C3 x 3! = 14400


3 particular boys are seperated

use ‘slotting’ method

6C3 is the number of ways the 3 PARTICULAR boys can be ‘slotted’




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