Quantitative Aptitude Ques 2250

Question: If a 4 digit number is formed at random using the digits 1, 3, 5, 7 and 9 without repetition, thus the probability that it is divisible by 5 is

Options:

A) $ \frac{4}{5} $

B) $ \frac{3}{2} $

C) $ \frac{1}{5} $

D) $ \frac{2}{3} $

Show Answer

Answer:

Correct Answer: C

Solution:

  • Number of four-digit numbers which are formed with $ 1, $ $ 3, $ $ 5, $ $ 7, $ $ 9={}^{5}P _4 $ $ =5\times 4\times 3\times 2=120=n(s) $ The number which are divisible by $ 5={}^{4}P _3 $ $ =4\times 3\times 2=24=n(E) $

$ \therefore $ $ P(E)=\frac{n(E)}{n(S)}=\frac{24}{120}=\frac{1}{5} $

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