A committee consisting of 6 people is to be selected from eight parents and four teachers Find the probability of selecting three parents and three teachers?
8/33
To find the probability of selecting three parents and three teachers out of a committee consisting of 6 people, we need to determine the total possible number of committees and the number of committees that meet the desired criteria.
First, we need to find the total number of committees. Since we are selecting 6 people from a group of 8 parents and 4 teachers, we can use the combination formula:
Total number of committees = (number of ways to select 6 from 12) = 12 C 6
This can be calculated using the formula: nCr = n! / (r!(n-r)!)
So, 12 C 6 = 12! / (6!(12-6)!) = 924
Now, we need to calculate the number of committees with 3 parents and 3 teachers. We can also use the combination formula for this:
Number of committees with 3 parents and 3 teachers = (number of ways to select 3 parents from 8) * (number of ways to select 3 teachers from 4)
So, (8 C 3) * (4 C 3) = (8! / (3!(8-3)!)) * (4! / (3!(4-3)!)) = (56) * (4) = 224
Finally, we can calculate the probability by dividing the number of desired committees by the total number of committees:
Probability = (Number of committees with 3 parents and 3 teachers) / (Total number of committees)
Probability = 224 / 924
Hence, the probability of selecting three parents and three teachers from the committee is 224/924, which simplifies to 28/77.