Answer: The correct option is (a) 12.
Step-by-step explanation: We are given to find the number of two-digit positive integers that can be formed from the digits 1, 3, 5, and 9, if no digit is repeated.
Here, we have 4 digits, out of which we have to choose the digits for the two places.
For first place, we have 4 options.
Since no digit is repeated, so we have 3 options for the second place.
Therefore,
the number of two-digit positive integers that can be formed from the digits 1, 3, 5, and 9, if no digit is repeated is given by the permutation of 4 digits taken 2 at a time.
Thus, the total number of two-digit positive integers will be
[tex]n=^4P_2=\dfrac{4!}{(4-2)!}=\dfrac{4!}{2!}=\dfrac{4\times3\times2!}{2!}=12.[/tex]
Option (a) is CORRECT.
