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14.Probability
hard
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
A
$30$
B
$33$
C
$40$
D
$43$
(JEE MAIN-2022)
Solution
$2 \;\times\; 2 \;\times \;2 \;\times \;2\; \times \;2 \;\times \;2\;=\;64$
Divisible by $21$ when divided by $3$ .
Case – $I$ : All $1 \rightarrow$ $(1)$
Case – $II$ : All $8 \rightarrow$ $(1)$
Case – $III$ : $3$ ones and $3$ eights
$\frac{6 !}{3 ! \times 3 !}=20$
Required probability $\therefore p =\frac{22}{64}$
$96 p =96 \times \frac{22}{64}=33$
Standard 11
Mathematics
