JEE Main 2022 · 26 Jun · Shift 2 · Mathematics Q30

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MathematicsInteger+4 / -1Question 30 of 90

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 $96p$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 33

Divisible by 3. With $k$ eights the digit sum is $6+7k\equiv k\pmod3$ , so $k\in\{0,3,6\}$ .

Divisible by 7. $8\equiv1\pmod7$ , so every such number $\equiv111111=7\times15873\equiv0$ .

Count. $1+\binom63+1=22$ of the $2^6=64$ numbers: $p=\frac{22}{64}$ , $96p=33$ .

Answer: 33

Topics:Classical probability Number systems

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JEE Main 2022 · 26 Jun · Shift 2, Mathematics question 30