Question

Two digits numbers are to be made using the digits $3,5,6$ and $8$ without repetition of digits. Find the probability of the following events.
The number is odd.
The number is divisible by $9$.

Answer 1

There are $4$ digits ,which ca be used.

No. of odd numbers are two i.e $3$&$5$

There is no number which is divisible by $9$.

Also we know that,

odd numbers end with odd digits.

Now total number that can be made by these $4$ digits $=4\times 3=12$

(a) probability of a odd number $=\frac{3\times 2}{12}=\frac{6}{12}$

$=\frac{1}{2}$

(b) Now,

Since sum of 3,5,6,8 is not divisible by $9$,

$\therefore$ the probability in that case will be $Zero$.