Find the probability that a randomly chosen 5-digit number is made from exactly two digits…

Question

Find the probability that a randomly chosen 5-digit number is made from exactly two digits.

Accepted Answer

Total 5-digit numbers $=9\times10^4$. Favourable: choosing 2 digits (one nonzero as leading) and counting arrangements using both, gives ${}^9C_2(2^5-2)+{}^9C_1(2^4-1) = 36(30)+9(15) = 1080+135=1215$.

$$P = \frac{1215}{90000} = \frac{135}{10000}$$

Solutions · 1