Find the probability that a committee of 10 people chosen from an organization consisting of 40 doctors and 35 dentists will include 3 doctors and 7 dentist.
40c10 + 35c10 not sure what to do after setting it up. Need help
it's a binomial expansion
(r + t)¹⁰ ... you want the 8th term
10C7 [(40/75)³ (35/75)⁷]
To find the probability of selecting a committee with 3 doctors and 7 dentists from a pool of 40 doctors and 35 dentists, you'll need to use combinations and probabilities.
First, let's calculate the number of ways to select 3 doctors out of 40 and 7 dentists out of 35.
The number of ways to select 3 doctors out of 40 can be calculated using the combination formula as follows:
40C3 = 40! / (3! * (40-3)!)
Similarly, the number of ways to select 7 dentists out of 35 can be calculated as:
35C7 = 35! / (7! * (35-7)!)
Now, to find the probability of selecting exactly 3 doctors and 7 dentists, you need to divide the number of ways to select this combination by the total number of possible combinations of selecting a committee of 10 people from the total pool of doctors and dentists.
The total number of possible combinations to select a committee of 10 people out of 75 (40 doctors + 35 dentists) can be calculated as:
75C10 = 75! / (10! * (75-10)!)
Finally, the probability of selecting exactly 3 doctors and 7 dentists is:
Probability = (40C3 * 35C7) / 75C10
To further simplify the calculations, you can use a calculator or software that can handle factorial calculations, or you can use approximations, such as Stirling's approximation, for large factorials.