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chrisyuen
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Homework Statement
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)
Homework Equations
Formulae for Bernoulli, Binomial, Geometric & Poisson Distributions
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!
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