A group of 10 students consisting of 5 boys and 5 girls are to be randomly divided into 5 pairs for a laboratory experiment. The probability that every pair consists of exactly one boy and one girl is :

Step-by-step solution

The total number of ways to divide 10 students into 5 unordered pairs is: Total ways = 10! (2!)^5 5! = 945 For each pair to consist of exactly one boy and one girl, we can think of the 5 boys as fixed and we must assign one of the 5 girls to each boy. The number of ways to do this is simply the number of permutations of the 5 girls: Favorable ways = 5! = 120 Thus, the required probability is: P = 120 945 = 24 189 = 8 63 Alternatively, using conditional probability for sequential pairing: P = ⁵C₁ ⁵C₁ ¹⁰C₂ ⁴C₁ ⁴C₁ ⁸C