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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