Statistics And Probability Question 214
Question: A three digit number is formed by using numbers 1, 2, 3 and 4. The probability that the number is divisible by 3, is
Options:
A) $ \frac{2}{3} $
B) $ \frac{2}{7} $
C) $ \frac{1}{2} $
D) $ \frac{3}{4} $
Show Answer
Answer:
Correct Answer: C
Solution:
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Total number of ways to form the numbers of three digit with 1, 2, 3 and 4 are $ {}^{4}P_3=4\,!=24 $ If the numbers are divisible by three then their sum of digits must be 3, 6 or 9 But sum 3 is impossible. Then for sum 6, digits are 1, 2, 3 Number of ways $ =3\,! $ Similarly for sum 9, digits are 2, 3, 4. Number of ways =3! Thus number of favorable ways $ =3\,!+3\,! $ Hence required probability $ =\frac{3\,!\,+\,3\,!}{4\,!}=\frac{12}{24}=\frac{1}{2}. $
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