Verified Solution • 2025–26 Session moderate

QJEEM23Maf381: JEE Main 2023 Mathematics - Class 12 JEEM23Maf381 Solution: Three dice are rolled. If the probability of getting different…

Three dice are rolled. If the probability of getting different numbers on the three dice is pq\frac{p}{q} , where pp and qq are co-prime, then q−pq-p is equal to :

Multiple Choice Options

  • A 3
  • B 4
  • C 1
  • D 2

Step-by-Step Verified Solution

Total number of outcomes =6×6×6=216=6 \times 6 \times 6=216

Number of outcomes getting different numbers on the three dice are 6P3=6!3!=120{ }^6 P_3=\frac{6 !}{3 !}=120

∴\therefore Required probability =120216=59=\frac{120}{216}=\frac{5}{9}

∴p=5\therefore p=5 and q=9q=9

∴q−p=9−5=4\therefore q-p=9-5=4

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