given: bag which contains 4 red, 5 black and 7 white balls

formula:

two balls are drawn at random, therefore

total possible outcomes are ¹⁶C₂

therefore n(S)=120

(i) let E be the event of getting both white balls

E= {(W) (W)}

n(E)= ⁷C₂=21

(ii) let E be the event of getting one black and one red ball

E= {(B) (R)}

n(E)= ⁵C₁⁴C₁=20

(iii) let E be the event of getting both balls of same colour

E= {(B) (B)} or {(W) (W)} or {(R) (R)}

n(E)= ⁷C₂+⁵C₂+⁴C₂=37