If a person has 3 coins of different denomina | vedclass

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(B) Given that a person has $3$ coins of different denominations.To form a sum,the person can choose $1, 2,$ or $3$ coins.The number of ways to select

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(B) Given that a person has $3$ coins of different denominations.To form a sum,the person can choose $1, 2,$ or $3$ coins.The number of ways to select $1$ coin out of $3$ is ${}^3C_1 = 3$.The number of ways to select $2$ coins out of $3$ is ${}^3C_2 = 3$.The number of ways to select $3$ coins out of $3$ is ${}^3C_3 = 1$.Since each combination of coins results in a unique sum (as denominations are different),the total number of different sums is ${}^3C_1 + {}^3C_2 + {}^3C_3 = 3 + 3 + 1 = 7$.

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

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