Question

The number of ways in which $3$ prizes can be distributed to $4$ children, so that no child gets all the three prizes, are

• A. 64
• B. 62
• C. 60
• D. None of these

Answer 1

Answer: (C)

Each of the three prizes can be given to any of the four children.
$\therefore $ Total number of ways of distributing prizes
$= 4 \times 4 \times 4 = 64$
Number of ways in which one child gets all prizes $= 4$
$\therefore $ Number of ways in which no child gets all the three prizes $= 64 - 4 = 60$