Verified Solution • 2025–26 Session moderate

QJEEM23Mac247: JEE Main 2023 Mathematics - Class 12 JEEM23Mac247 Solution: Fifteen football players of a club-team are given 15 T-shirts…

Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least 3 players pick the correct T-shirt is :

Multiple Choice Options

  • A 16
  • B 215
  • C 524
  • D 0.08

Step-by-Step Verified Solution

Required probability =1−D(15)+15C1⋅D(14)+15C2D(13)15!=1-\frac{D_{(15)}+{ }^{15} C_1 \cdot D_{(14)}+{ }^{15} C_2 D_{(13)}}{15 !}

Taking D(15)\mathrm{D}_{(15)} as 15!e\frac{15 !}{e}

D(14)\mathrm{D}_{(14)} as 14 ! e\frac{14 \text { ! }}{e}

D(13)\mathrm{D}_{(13)} as 13 ! e\frac{13 \text { ! }}{e}

 We get,  Required probability =1−(15!e+15⋅14!e+15×142×13!e15!)

=1−(1e+1e+12e)=1−52e≈.08

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