JEE MAIN - Mathematics (2022 - 26th June Evening Shift - No. 22)

If the probability that a randomly chosen 6-digit number formed by using digits 1 and 8 only is a multiple of 21 is p, then 96 p is equal to _______________.
Answer
33

Explanation

Total number of numbers from given

Condition = n(s) = 26.

Every required number is of the form

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

Here 111111 is always divisible by 21.

$$\therefore$$ If A is divisible by 21 then

10a1 + 10a2 + 10a3 + ....... 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 = $${{22} \over {{2^6}}} = p$$

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

$$\therefore$$ $$96p = 33$$

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