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Question
A four digit number is formed using the digits 1, 2, 3, 5 with no repetitions. Write the probability that the number is divisible by 5.
Solution
\[\text{ To be divisible by 5 ones place sholud be } 5\]
\[\text{ There are 3 places remaining which can be filled in 3 ! = 6ways } \]
\[\text{ So, 6 numbers can be formed out of 1, 2, 3 and 5, which are divisible by 5 } . \]
\[\text{ Total 4-digit numbers = 4! = 24} \]
\[P\left( \text{ 4-digit number divisible by 5 } \right) = \frac{6}{24}\]
\[ = \frac{1}{4}\]
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