Let us name the boys as B1andB2
, and the girls as G1,G2andG3
.
Then
S={B1B2,B1G1,B1G2,B1G3,B2G1,B2G2,B2G3,G1G2,G1G3,G2G3}
We have
(i) A={G1G2,G1G3,G2G3}
(ii) B={B1G1,B1G2,B1G3,B2G1,B2G2,B2G3}
(iii) C={B1G1,B1G2,B1G3,B2G1,B2G2,B2G3,B1B2}
Clearly, A∩B=ϕandA∩C=ϕ
.
Hence, (A, B) and (A, C) are mutually exclusive events.