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3 dolls, 4 kitchen sets and 3 cars are displayed in a toy shop. In how many ways can 3 toys be selected such that,

(i) all are dolls?
(ii) all are different toys?
(iii) two are dolls and one is a kitchen set?

1 Answer

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Best answer

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

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