3 dolls, 4 kitchen sets and 3 cars are displayed in a toy shop. 3 toys are to be selected.
(i) All are dolls : There are 3 dolls.
∴ Total combinations = 3C3 = 1
(ii) All are different toys: One doll out of 3 dolls can be selected in 3C1 ways and one kitchen set out of 4 sets can be selected in 4CX ways and one car out of 3 cars can be selected in 3C1 ways.
∴ Total combinations = 3C1 × 4C1 × 3C1 =3x4x3 = 36
(iii) Two are dolls and one is a kitchen
set: Two dolls out of 3 dolls can be selected in 3C2 ways and one kitchen set out of 4 sets can be selected in 4C1 ways.
∴ Total combinations = 3C2 × 4C1
= \(\frac{3×2}{2×1} × 4\)
= 3 × 4
= 12