Probability
Probability
Allen Star Batch
Grade 12
Question:
Out of 6 pairs of distinct gloves 8 gloves are randomly selected, then the probability that there exist exactly 2 pairs in it is :
$\frac{16}{33}$
$\frac{1}{3}$
$\frac{12}{33}$
$\frac{10}{33}$
Step-by-Step Solution
Key Concept: Count distributions using combinations to allocate balls to boxes with the required constraint.
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