a, b, c are three distinct integers from 2 to 10 (both inclusive). Exactly one of ab, bc and ca is odd. abc is a multiple of 4. The arithmetic mean of a and b is an integer and so is the arithmetic mean of a, b and c. How many such triplets are possible (unordered triplets) ?  Choose the correct choice from the following answers:
A) 3 B) 4 C) 5 D) 2 E) 1
Explanation :   Exactly one of ab, bc and ca is odd⇒ Two are odd and one is evenabc is a multiple of 4⇒ the even number is a multiple of 4The arithmetic mean of a and b is an integer⇒ a and b are oddand so is the arithmetic mean of a, b and c.⇒ a+ b + c is a multiple of 3c can be 4 or 8.c = 4; a, b can be 3, 5 or 5, 9c = 8; a, b can be 3, 7 or 7, 9Four triplets are possible   Answer : 4
<result>B</result>
a, b, c are three distinct integers from 2 to 10 (both inclusive). Exactly one of ab, bc and ca is odd. abc is a multiple of 4. The arithmetic mean of a and b is an integer and so is the arithmetic mean of a, b and c. How many such triplets are possible (unordered triplets) ?