Question

Using the digits 0,1,2,3,4,5,6, how many 4 digit even numbers can be made, no digit being repeated?

Answer 1

Given: digit 0, 1, 2, 3, 4, 5 and 6 

Number of 4 digit even number ending with zero are = ⎕ ⎕ ⎕ ⌻ 

= ⁶P₃ × ¹P₁ 

= \(\frac{6!}{3!}\)× 1 = \(\frac{720}{6}\) = 120 

Number of 4 digit even number ending with 2,4 and 6 are 

= 5 × 5 × 4 × 3 

= 300 

Total number of 4 digit even numbers using 0,1,2,3,4,5,6 = 300 + 120 

= 420