Out of 6 pairs of distinct gloves 8 gloves are randomly selected, then the probability that there exist exactly 2 pairs in it is :
Step-by-Step Solution
Key Concept: To find the probability of exactly 2 complete pairs among 8 selected gloves from 6 pairs: calculate favorable outcomes where exactly 2 pairs are complete (both gloves selected) and remaining 4 gloves form 0 complete pairs, then divide by total ways C(12,8) = C(12,4) = 495.
Favorable cases where all 6 balls are distributed among at least 3 boxes with at least one ball in each: $m = ^6C_4(2^4) + 2^6C_1(^6C_1) + ^6C_2(^6C_2) = 16$. Total cases: $n = ^{12}C_6$. The probability is $ rac{m}{n} = rac{16}{33}$.
Correct Answer: 1