Probability
Counting and Probability
Grade 12
Question:
<p>Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3. Then, probability of event A is equal to</p>
<p>(a) \(\frac{9}{56}\)</p>
<p>(b) \(\frac{4}{9}\)</p>
<p>(c) \(\frac{3}{7}\)</p>
<p>(d) \(\frac{11}{27}\)</p>
Step-by-Step Solution
Key Concept: A number is divisible by 3 if the sum of its digits is divisible by 3. Count favorable arrangements and divide by total arrangements.
<p><strong>Solution:</strong> The question requires finding the probability that a 6-digit integer formed from {0, 1, 2, 3, 4, 5, 6} without repetition is divisible by 3. The answer is $\frac{4}{9}$.</p>
Correct Answer: b