1. The problem statement, all variables and given/known data At a school sports day, the timekeeping group for running events consists of 1 chief judge, 1 referee and 10 timekeepers. The chief judge and the referee are chosen from 5 teachers while the 10 timekeepers are selected from 16 students. (a) How many different timekeeping groups can be formed? (b) If it is possible to have a timekeeping group with all the timekeepers being boys, what are the possible numbers of boys among the 16 students? (c) If the probability of having a timekeeping group with all the timekeepers being boys is 3 / 364, find the number of boys among the 16 students. (Answers: (a) 160160; (b) 10, 11, 12, 13, 14, 15, 16 (c) 12) 2. Relevant equations Formulae for Bernoulli, Binomial, Geometric & Poisson Distributions 3. The attempt at a solution I don't know how to solve part (c) of the question. I tried: xC10 / 16C10 = 3 / 364 and x can be found as 12. I don't know if the above method is correct or not. However, the question should be solved using the distribution formulae. Another attempt: x: number of boys within the 16 students P(Boys) = x / 16 16C10 (x / 16)10 (1 - x / 16)6 = 3 / 364 But the x found is not correct. Can anyone tell me how to solve it? Thank you very much!