Question

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

A
B
C
D
##### 28
Solution

Correct option is

(B)

a + b + c = 10 , Let us place 10 sticks in a row

| | | | | | | | | |

now place two " + "

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

This will become 4 + 5 + 1 , OR , a = 4 , b = 5 , c = 1

hence we hace 9 slots out of which 2 has to be selected for " + " s

now , number of ways = $9C_2$ = 36

hence B is the correct option