Question

What is the total number of even non-negative integers that can be formed by using the digits 0, 1, 3, 5, 7 and 9, where repetition of digits isnotallowed?

• 325

• 326

• 1405

• 1406

Ans :

Number of 1-digit even numbers = 0

Number of 2-digit even numbers = 5×1 = 5

Number of 3-digit even numbers = 5×4×1 = 20

Number of 4-digit even numbers = 5×4×3×1 = 60

Number of 5-digit even numbers = 5×4×3×2×1 = 120

Number of 6-digit even numbers = 5×4×3×2×1×1 = 120

Note:Here, the units place digit is always occupied by 0.

Total number of even non-negative integers that can be formed by using digits 0, 1, 3, 5, 7 and 9, where repetition of digits is not allowed = 0 + 5 + 20 + 60 + 120 + 120 = 325

The correct answer is given by option A.

AS UNDERLINED ABOVE,0 IS AN EVEN NON NEGATIVE INTEGER.WHY AREN'T WE CONSIDERING IT

Answer 1

$$\begin{gathered} \mathrm{Hi}, \\ 0\mathrm{is}\mathrm{even}\mathrm{but}\mathrm{it}\mathrm{is}\mathrm{neither}\mathrm{negative}\mathrm{nor}\mathrm{positive}\mathrm{so}\mathrm{that}\mathrm{is}\mathrm{why}\mathrm{we}\mathrm{are}\mathrm{not}\mathrm{considering} \\ \mathrm{it}. \end{gathered}$$