Passage: A 4-digit number is selected at random formed by using the...

The total number of $4$-digit numbers formed using the digits $0, 1, 2, 3, 4$ without repetition is calculated by filling the thousands place in $4$ ways (excluding $0$) and the remaining $3$ places in ^{4}P_{3}$ways.<br><br>Total outcomes = 4 \times 4 \times 3 \times 2 = 96$

The number of $4$-digit numbers formed without using $0$ at any position means using only the digits $1, 2, 3, 4$.

Favorable outcomes = ^{4}P_{4} = 4 \times 3 \times 2 \times 1 = 24$<br><br>Required probability = \dfrac{24}{96} = \dfrac{1}{4} = 0.25$

Answer: $0\cdot25$