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

 

Solution

(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

note: 

3 particular boys are seperated

use ‘slotting’ method

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

 

 

 

Leave a Reply

Your email address will not be published. Required fields are marked *