Question

In how many ways can $14$ identical toys be distributed among $3$ boys such that everyone gets at least one toy and no two boys get an equal number of toys.

• A. $65$
• B. $62$
• C. $60$
• D. $70$

Answer 1

The correct option is C $60$

Possible distribution:

$\left\{\mathrm{1.2.11}\right\};\{1,3,10\};\{1,4,9\}\{1,5,8\};\{1,6,7\};\{2,3,9\}\{2,4,8\};\{2,5,7\};\{3,4,7\}\{3,5,6\}$

Number of options $=10$

Each option can be arranged in $3!$ ways

Total ways of distribution $(3!\times 10)=60$ Ways

Hence the correct answer is $60$ Ways.