Question

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

CORRECT ANSWER WRONG ANSWER

CORRECT ANSWER WRONG ANSWER

CORRECT ANSWER WRONG ANSWER

CORRECT ANSWER WRONG ANSWER

Solution

Correct option is

(A)

Explanatory Answer

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 = ${12}C_{2}$ = 66

A is the correct option