QJEEM22Ma3043: JEE Main 2022 Mathematics - Class 12 JEEM22Ma3043 Solution: If the probability that a randomly chosen 6-digit number formed …

Total number of numbers from given

Condition = n(s) = 2⁶.

Every required number is of the form

A = 7 . (10^a₁ + 10^a₂ + 10^a₃ + .......) + 111111

Here 111111 is always divisible by 21.

$\therefore$ If A is divisible by 21 then

10^a₁ + 10^a₂ + 10^a₃ + ....... must be divisible by 3.

For this we have ⁶C₀ + ⁶C₃ + ⁶C₆ cases are there

$\therefore$ n(E) = ⁶C₀ + ⁶C₃ + ⁶C₆ = 22

$\therefore$ Required probability = ${{22} \over {{2^6}}} = p$

$\therefore$ ${{11} \over {32}} = p$

$\therefore$ $96p = 33$