If a person has 3 coins of different denominations, the number of different sums can be formed is

Given that person has $3$ coins of different denominations,

Selecting $1$ coin out of $3$ coins gives ${}^3{C}_1$ ways.

Selecting $2$ coin out of $3$ coins gives ${}^3{C}_2$ ways.

Selecting $3$ coin out of $3$ coins gives ${}^3{C}_3$ ways.

Total number of different sums of money that can person form is

${}^3{C}_1+{}^3{C}_2+{}^3{C}_3=3+3+1=7$ways