Question

In how many different ways can three persons A, B, C having $6,7$ and $8$ one rupee coins respectively donate $Rs.10$ collectively?

• A. $45$
• B. $46$
• C. $47$
• D. $48$

Answer 1

Answer: (C)

$47$

If $A$ donates $0$ coins then $B$ and $C$ combined can donate $10$ coins in $6$ ways

If $A$ donates $1$ coins then $B$ and $C$ combined can donate $9$ coins in $7$ ways

If $A$ donates $2$ coins then $B$ and $C$ combined can donate $8$ coins in $8$ ways

If $A$ donates $3$ coins then $B$ and $C$ combined can donate $7$ coins in $8$ ways

If $A$ donates $4$ coins then $B$ and $C$ combined can donate $6$ coins in $7$ ways

If $A$ donates $5$ coins then $B$ and $C$ combined can donate $5$ coins in $6$ ways

If $A$ donates $6$ coins then $B$ and $C$ combined can donate $4$ coins in $5$ ways

Total number of ways $A$ , $B$ , $C$ combined can donate $10$ coins is $6+7+8+8+7+6+5=47$

The correct option is $C$