SOLUTION: The Earth Sciences Club at Wild West College consists of ten geologists, nine astronomers, five biologists, and seven physicists. Four members of the club are to be chosen (at rand

Algebra ->  Probability-and-statistics -> SOLUTION: The Earth Sciences Club at Wild West College consists of ten geologists, nine astronomers, five biologists, and seven physicists. Four members of the club are to be chosen (at rand      Log On


   

Question 1185205: The Earth Sciences Club at Wild West College consists of ten geologists, nine astronomers, five biologists, and seven physicists. Four members of the club are to be chosen (at random) to attend a conference. What is the probability that four physicists will be chosen?
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.
The Earth Sciences Club at Wild West College consists of ten geologists, nine astronomers, five biologists, and seven physicists.
Four members of the club are to be chosen (at random) to attend a conference. What is the probability that four physicists will be chosen?
~~~~~~~~~~~~~~~~


I will show you two possible ways of solution.

Notice that the total people is 10 + 9 + 5 + 7 = 31. 


1)  Use the formula


        P = %287%2F31%29%2A%286%2F30%29%2A%285%2F29%29%2A%284%2F28%29 = reduce fraction = %287%2F31%29%2A%281%2F5%29%2A%285%2F29%29%2A%281%2F7%29 = 1%2F%2831%2A29%29 = 1%2F899 = 0.001112  (rounded).    ANSWER


    This formula is SELF-EXPLANATTORY.



2)  Another formula comes from COMBINATORICS.  It is self-explanatory, too.


        P = C%5B7%5D%5E4%2FC%5B31%5D%5E4 = 35%2F31465 = 1%2F899 = 0.001112  (rounded).    ANSWER


    giving the same answer.


    In this formula, the numerator is the number of all favorable quadruples of 4 physicist; 

    the denominator is the total number of quadruples of 31 persons.

Solved.