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14.Probability
hard
A seven digit number is formed using digits $3 ,3,4,4,4,5,5 .$ The probability, that number so formed is divisible by $2,$ is ..... .
A
$\frac{6}{7}$
B
$\frac{1}{7}$
C
$\frac{3}{7}$
D
$\frac{4}{7}$
(JEE MAIN-2021)
Solution
Digits $=3,3,4,4,4,5,5$
Total $7$ digit numbers $=\frac{7 !}{2 ! 2 ! 3 !}$
Number of $7$ digit number divisible by $2$ $\Rightarrow$ last digit $=4$
Now $7$ digit numbers which are divisible by $2$
$=\frac{6 !}{2 ! 2 ! 2 !}$
Required probability $=\frac{\frac{6 !}{2 ! 2 ! 2 !}}{\frac{7 !}{3 ! 2 ! 2 !}}=\frac{3}{7}$
Standard 11
Mathematics
