MCQ
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$\frac{1}{7}$
- ✓$\frac{3}{7}$
- D$\frac{4}{7}$
✓
Answer
Correct option: C.
$\frac{3}{7}$
c
Digits $=3,3,4,4,4,5,5$
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 $=\frac{\frac{6 !}{2 ! 2 ! 2 !}}{\frac{7 !}{3 ! 2 ! 2 !}}=\frac{3}{7}$
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