The probability that a randomly chosen 5-digit number is made fro… - Vidyadip

MCQ

The probability that a randomly chosen $5-digit$ number is made from exactly two digits is

A
$\frac{121}{10^{4}}$
B
$\frac{150}{10^{4}}$
✓
$\frac{135}{10^{4}}$
D
$\frac{134}{10^{4}}$

✓

Answer

Correct option: C.

$\frac{135}{10^{4}}$

c
First Case: Choose two non-zero digits ${ }^{9} C _{2}$

Now, number of 5 -digit numbers containing both digits $=2^{5}-2$

Second Case: Choose one non-zero \& one zero as digit ${ }^{9} C _{1}$

Number of 5 -digit numbers containg one non zero and one zero both $=\left(2^{4}-1\right)$ Required prob.

$=\frac{\left({ }^{9} C _{2} \times\left(2^{5}-2\right)+{ }^{9} C _{1} \times\left(2^{4}-1\right)\right)}{9 \times 10^{4}}$

$=\frac{36 \times(32-2)+9 \times(16-1)}{9 \times 10^{4}}$

$=\frac{4 \times 30+15}{10^{4}}=\frac{135}{10^{4}}$

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