Probability Question 403

Question: Five digit numbers are formed using the digits 1, 2, 3, 4, 5, 6 and 8. What is the probability that they have even digits at both the ends

[RPET 1999]

Options:

A) $ \frac{2}{7} $

B) $ \frac{3}{7} $

C) $ \frac{4}{7} $

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

  •                 By using digits 1, 2, 3, 4, 5, 6 and 8, total 5 digits numbers =  $ ^{7}P_5 $                     And number of ways to form the numbers, they have even digit at both ends  $ =4\times 3{{\times }^{5}}P_3 $                      
    

$ \therefore $ Probability $ =\frac{4\times 3{{\times }^{5}}P_3}{^{7}P_5}=\frac{2}{7} $ .



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