# Total number of 6-digit numbers

Question:

Total number of 6-digit numbers in which only and all the five digits $1,3,5,7$ and 9 appear, is:

1. (1) $\frac{1}{2}(6 !)$

2. (2) $6 !$

3. (3) $5^{6}$

4. (4) $\frac{5}{2}(6 !)$

Correct Option: , 4

Solution:

Five digits numbers de $1,3,5,7,9$

For selection of one digit, we have ${ }^{5} C_{1}$ choice.

And six digits can be arrange in $\frac{6 !}{2 !}$ ways.

Hence, total such numbers $=\frac{5.6 !}{2 !}=\frac{5}{2} \cdot 6 !$