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

Question

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

Accepted Answer

Sample space = 9 $$ \times $$ 104

Case - I

Out of exactly two digits selected one is zero then favourable cases = ${}^9{C_1}({2^4} - 1)$

Case - II

Both selected digits are non-zero then favourable cases = ${}^9{C_2}({2^5} - 2)$

Probability = $${{9({2^4} - 1) + {{9.8} \over 2}({2^5} - 2)} \over {9 \times {{10}^4}}}$$

$$ = {{15 + 120} \over {{{10}^4}}} = {{135} \over {{{10}^4}}}$$

Solutions · 1