Question

In how many ways can $15$ blankets be distributed among $6$ beggars such that everyone gets at least one blanket and two particular beggars get equal blankets and another three particular beggars get equal blankets.

• A. $21$
• B. $24$
• C. $25$
• D. $12$

Answer 1

The correct option is D $12$

The following are the possible distribution patterns:-

SI. No. Beggar $1$ Beggar $2$ Beggar $3$ Beggar $4$ Beggar $5$ Beggar $6$

$1)$ $1$ $1$ $1$ $4$ $4$ $4$

$2)$ $1$ $4$ $4$ $2$ $2$ $2$

$3)$ $2$ $2$ $2$ $2$ $2$ $2$

$4)$ $2$ $5$ $5$ $1$ $1$ $1$

$5)$ $3$ $3$ $3$ $2$ $2$ $2$

$6)$ $4$ $1$ $1$ $3$ $3$ $3$

$7)$ $4$ $4$ $4$ $1$ $1$ $1$

$8)$ $5$ $2$ $2$ $2$ $2$ $2$

$9)$ $6$ $3$ $3$ $1$ $1$ $1$

$10)$ $7$ $1$ $1$ $2$ $1$ $1$

$11)$ $8$ $2$ $2$ $1$ $1$ $1$

$12)$ $10$ $1$ $1$ $1$ $1$ $1$