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’*