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A four digit number is formed by the digits 1,2 , 3,4 with no repetition. The probability that the number is odd, is
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The correct answer is:
None of these
Given digits are $1,2,3,4$.
Possibilities for units 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 $=1$
$\therefore \quad$ Number of favourable outcomes $=2 \times 3 \times 2 \times 1=12$
Number of numbers formed by $1,2,3,4$
(without repetitions) $=4 !$
$\therefore \quad$ Required probability $=\frac{12}{4 \times 3 \times 2}=\frac{1}{2}$
Possibilities for units 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 $=1$
$\therefore \quad$ Number of favourable outcomes $=2 \times 3 \times 2 \times 1=12$
Number of numbers formed by $1,2,3,4$
(without repetitions) $=4 !$
$\therefore \quad$ Required probability $=\frac{12}{4 \times 3 \times 2}=\frac{1}{2}$
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