Question

A person has 4 coins each of different denomination. What is the number of different sums of money the person can form (using one or more coins at a time

Answer 1

Answer:

15

Step-by-step explanation:

To select 1 coin out of 4 coins:   ⁴C₁ = 4 Different sums  possible

Selecting 2 coins out of 4 coins:  ⁴C₂ = 6 different sums  possible

Selecting 3 coins out of 4 coins: ⁴C₃ = 4 different sums  possible

Selection 4 coins out of 4 coins: ⁴C₄ =1 sum  possible

Hence total number of different sums are  : 4 + 6 + 4 + 1 =  15

Please note:- There is a possibility that sums produced by 1 set overlap with sum produced by 2nd set. To determine that exact overlap actual denominations are required which is missing in question.

Answer 2

Answer:

Number of different sums of money that can person form is 15.

Step-by-step explanation:

Given : A person has 4 coins each of different denomination.

To find : What is the number of different sums of money the person can form?

Solution :

A person has 4 coins each of different denomination.

Selecting 1 coin out of 4 coins gives $^4C_1$ possible ways.  

Selecting 2 coin out of 4 coins gives $^4C_2$ possible ways.  

Selecting 3 coin out of 4 coins gives $^4C_3$ possible ways.  

Selecting 4 coin out of 4 coins gives $^4C_4$ possible ways.  

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

$T=^4C_1+^4C_2+^4C_3+^4C_4$

$T=4+6+4+1$

$T=15$

Therefore, Number of different sums of money that can person form is 15.