# If four digit numbers greater than 5000 are randomly formed from the digits 0,1,3,5 and 7,what is the probability of forming number divisible by 5 when repetition of digits is not allowed.

$\begin{array}{1 1}(A)\;\large\frac{3}{8}\\(B)\;\large\frac{3}{5}\\(C)\;\large\frac{4}{7}\\(D)\;\large\frac{7}{8}\end{array}$

## 1 Answer

Toolbox:
• Required probability=$\large\frac{n(E)}{n(S)}$
Step 1:
4 digit number greater than 5000 are to be formed
Digits -0,1,3,5,7
Number to be divisible by 5
$\therefore$ A number can be divisible by 5 only when its units digit is 0,5
Step 2:
Since the number have to be greater than 5000.The thousand place will be 5 or 7 and the rest three digits will have options of 4,3,2 outcomes respectively.
$\therefore$ Total number of outcomes n(S)=24+24=48
Step 3:
Number of favorable outcomes :
For a number to be divisible by 5.The unit digit should be 0 or 5.The unit digit should be 0 or 5 and thousands digits are 5 or 7.
$\therefore$ Options for tens and hundreth digits are 3 and 2.
$\therefore$ Favorable outcomes n(E)=6+6+6=18
Step 4:
$\therefore$ Required probability =$\large\frac{n(E)}{n(S)}$
$\Rightarrow \large\frac{18}{48}$
$\Rightarrow \large\frac{3}{8}$
Hence (A) is the correct answer.
answered Jul 7, 2014

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