JEE PYQ: Probability Question 18
Question 18 - 2020 (03 Sep Shift 2)
The probability that a randomly chosen 5-digit number is made from exactly two digits is:
(1) $\frac{135}{10^4}$
(2) $\frac{121}{10^4}$
(3) $\frac{150}{10^4}$
(4) $\frac{134}{10^4}$
Show Answer
Answer: (1)
Solution
Total 5-digit numbers: $9 \times 10^4$. Choose 2 digits and count 5-digit numbers using exactly both. Numbers using at most 2 specific digits minus those using exactly 1: ${}^9C_1(2^5 - 2) + {}^9C_1 \cdot {}^9C_1(2^4 - 1) = …$. After careful counting: $P = \frac{135}{10^4}$.
BETA
