Question

A four digit number is formed by the digits $1, 2, 3, 4$ with no repetition. The probability that the number is odd, is

• A. 0
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. None of these

Answer 1

The Correct Option is D

Given numbers are $1,2,3,4$
Possibilities for unit's place digit (either 1 or 3 )
$=2$
Possibilities for ten's digit $=3$
Possibilities for hundred's place digit $=2$
Possibilities for thousand' place's digit = 1
$\therefore$ Number of favourable outcomes
$=2 \times 3 \times 2 \times 1=12$
Number of numbers formed by $1,2,3,4$ (without repetitions) $=4 !$
$\therefore$ Required probability $=\frac{12}{4 \times 3 \times 2}=\frac{1}{2}$