Question

The Number Of Ways In Which One Can Select Three Distict Integers Between 1 And30 Both Inclusive Whose Sum Is Even Is

Answer 1

Answer:Number are either all even or one even and other two odd.

Required number of ways =15C3+15C1×15C2

15C3=15!3!12!=15×14×13×12!3×2×12!

⇒455

15C1=15!1!×14!

⇒15

15C2=15!2!×13!

⇒105

15C3+15C1×15C2=455+15×105

⇒455+1575

⇒2030

Explanation:

Answer 2

The required number of ways = 15C3 + 15C1 × 15C2

Explanation:

Numbers are either all even or one even and other two odd.

Required number of ways = 15C3 + 15C1 × 15C2

15C3 = 15! 3! 12! = 15 × 14 × 13 × 12! 3 × 2 × 12!

⇒ 455

15 C1 = 15! 1! × 14!

⇒ 15

15C2=15!2!×13!

⇒105

15C3 + 15C1 × 15C2 = 455 + 15 × 105

⇒ 455 + 1575

⇒ 2030