Question

# Sum of three Whole numbers a, b and c is 10. How many ordered triplets (a, b, c) exist

A
B
C
D
##### 56
Solution

Correct option is

(A)

a , b , c are whole numbers such that , a+b+c=10

if we remove the constraints that , a , b, c can be zero

And if we give a minimum of 1 to a , b , c ,

then we can use the original approach , And then we can finally remove 1 from each , ( a, b , c)

Let distribute 13 sticks across , a, b, c.

and the finally remove 1 from each

a + b+ c = 13. Let Place 10 sticks in a row

| | | | | | | | | |

now we will place two "+" , for eg :

| | | | + | | | | | + | | | |

this will equivalent of 4+5+4 , OR ,

a = 4 , b = 5 , c = 4

Now there are 12 slots between sticks , out of which , one has to select b 2 for placing the , " + ""

so , number of ways = $&space;{12}C_{2}$ = 66

A is the correct option