Verified Solution • 2025–26 Session moderate

QJEEM20Ma7246: JEE Main 2020 Mathematics - Class 12 JEEM20Ma7246 Solution: The probability that a randomly chosen 5-digit number is made…

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

Multiple Choice Options

  • A 150104{{150} \over {{{10}^4}}}
  • B 134104{{134} \over {{{10}^4}}}
  • C 121104{{121} \over {{{10}^4}}}
  • D 135104{{135} \over {{{10}^4}}}

Step-by-Step Verified Solution

Sample space = 9 ×\times 104

Case - I

Out of exactly two digits selected one is zero then favourable cases = 9C1(24−1){}^9{C_1}({2^4} - 1)

Case - II

Both selected digits are non-zero then favourable cases = 9C2(25−2){}^9{C_2}({2^5} - 2)

Probability = 9(24−1)+9.82(25−2)9×104{{9({2^4} - 1) + {{9.8} \over 2}({2^5} - 2)} \over {9 \times {{10}^4}}}

=15+120104=135104= {{15 + 120} \over {{{10}^4}}} = {{135} \over {{{10}^4}}}

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