2004 · Q51
51. Four different toys are to be distributed among two children such that each child gets at least one toy. In how many different ways can this be done?
MathematicsCombinatorics
- A6
- B8
- C12
- D14
Explanation
Each of the 4 distinct toys can go to either child, giving 2⁴ = 16 distributions. Two of these give all four toys to one child, violating the "at least one toy each" condition. Subtracting them leaves 16 − 2 = 14 valid ways.