Question

a person X has four notes of rupee 1,2,5,10 denomination.the number of different sums of money she can form from them is?

Answer 1

= (taking one at a time) + (taking two at a time) + (taking three at a time) + taking four at a time)
= ⁴C1 + ⁴C2 + ⁴C3 + ⁴C4
= 4+6+4+1
=15

Answer 2

Answer:

Hence, the number of different sums of money she can form from them is:

15

Step-by-step explanation:

As a person has to make different sum of money using these four different notes of different denominations.

So, the possible ways he could do this is by making the following combinations:

1 , 2 , 5, 10 , 1+2 , 1+5 , 1+10 , 2+5 , 2+10 , 5+10 , 1+2+5 , 1+5+10 , 2+5+10 , 1+2+10 , 1+2+5+10

This means that there are total 15 cases.

Also this can be done by the method of combination.

i.e the different combinations possible are:

$=4_C_1+4_C_2+4_C_3+4_C_4\\\\=\dfrac{4!}{1!\times (4-1)!}+\dfrac{4!}{2!\times (4-2)!}+\dfrac{4!}{3!\times (4-3)!}+\dfrac{4!}{4!\times (4-4)!}\\\\=\dfrac{4!}{1!\times 3!}+\dfrac{4!}{2!\times 2!}+\dfrac{4!}{3!\times 1!}+\dfrac{4!}{4!\times 0!}\\\\=4+6+4+1\\\\=15$

Hence, the number of different sums of money she can form from them is:

15