Passage: A 4-digit number is selected at random formed by using the digits 0 , 1 , 2 , 3 and 4 (where repetition of digits is not allowed). Question: What is the probability that the number selected does not contain zero at any position ?

Step-by-step solution

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 ⁴P₃ ways. Total outcomes = 4 4 3 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 = ⁴P₄ = 4 3 2 1 = 24 Required probability = 24 96 = 1 4 = 0.25 Answer: 0 25