1. A committee of 10 is selected at random from a group of faculty members consi
ID: 3069087 • Letter: 1
Question
1. A committee of 10 is selected at random from a group of faculty members consisting of 15 from the Mathematics Department, 22 from the Chemistry Department, and 10 from the English Department Mathematics Department and 7 from the Chemistry Department? Mathematics Department and 3 from the English Department and 2 a. What is the probability that the committee will consist of 3 from the b. What is the probability that the committee will consist of 5 from the from the Chemistry department? c. What is the probability that the committee will consist of 3 from the Mathematics Department, 3 from the Chemistry Department, and 4 from the English Department?Explanation / Answer
We are need to form a committee of 10 people selected randomly from 15 Mathematics Department , 22 from the Chemistry Department and 10 from the English Department.
a) total number of possibilities is 47 C 10= 5178066751
total possibilities for 3 Mathematics department is 15 C 3= 455
total possibilities for 7 from chemistry department is 22C7= 170544
probability of this selection is ((15 C 3)*(22C 7))/(47C10).
= 455*170544/5178066751
= 0.0149858
b) total number of possibilities is 47 C 10= 5178066751
total possibilities for 5 Mathematics department is 15 C 5= 3003
total possibilities for 2 from chemistry department is 22C2=231
total possibilities for 3 from English department is 10C3= 120
probability of this selection is ((15 C 5)*(22C 2)*(10C 3))/(47C10)
= 3003*231*120/5178066751
= 0.016076
c) total number of possibilities is 47 C 10= 5178066751
total possibilities for 5 Mathematics department is 15 C 3= 455
total possibilities for 2 from chemistry department is 22C3=1540
total possibilities for 3 from English department is 10C4= 210
probability of this selection is ((15 C 3)*(22C 3)*(10C4))/(47C10).
= 455*1540*210/5178066751
= 0.028417
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