Medium MCQ +4 / -1 PYQ · JEE Mains 2020

The probability that a randomly chosen 5-digit number is made from exactly two digits is :

A ${{150} \over {{{10}^4}}}$
B ${{134} \over {{{10}^4}}}$
C ${{121} \over {{{10}^4}}}$
D ${{135} \over {{{10}^4}}}$ Correct answer

Solution

Sample space = 9 $\times$ 104 Case - I Out of exactly two digits selected one is zero then favourable cases = ${}^9{C_1}({2^4} - 1)$ Case - II Both selected digits are non-zero then favourable cases = ${}^9{C_2}({2^5} - 2)$ Probability = ${{9({2^4} - 1) + {{9.8} \over 2}({2^5} - 2)} \over {9 \times {{10}^4}}}$ $= {{15 + 120} \over {{{10}^4}}} = {{135} \over {{{10}^4}}}$

About this question

Subject: Mathematics · Chapter: Probability · Topic: Classical and Axiomatic Probability

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The probability that a randomly chosen 5-digit number is made from exactly two digits is :

Solution

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