Verified Solution • 2025–26 Session moderate

QJEEM20Ma4556: JEE Main 2020 Mathematics - Class 12 JEEM20Ma4556 Solution: Out of 11 consecutive natural numbers if three numbers are…

Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is :

Multiple Choice Options

  • A 1099{{10} \over {99}}
  • B 533{{5} \over {33}}
  • C 15101{{15} \over {101}}
  • D 5101{{5} \over {101}}

Step-by-Step Verified Solution

Out of 11 consecutive natural numbers either 6 even and 5 odd numbers or 5 even and 6 odd numbers.

Let, E = Even
O = Odd

Case-1 :

E, O, E, O, E, O, E, O, E, O, E

2b = a + c ⇒\Rightarrow Even

⇒\Rightarrow Both a and c should be either even or odd.

P = 6C2+5C211C3{{{}^6{C_2} + {}^5{C_2}} \over {{}^{11}{C_3}}} = 533{5 \over {33}}

Case -2 :

O, E, O, E, O, E, O, E, O, E, O

P = 5C2+6C211C3{{{}^5{C_2} + {}^6{C_2}} \over {{}^{11}{C_3}}} = 533{5 \over {33}}

Total probability = 12×533{1 \over 2} \times {5 \over {33}} + 12×533{1 \over 2} \times {5 \over {33}} = 533{5 \over {33}}

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