Question

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.

Answer 1

All in all, there are 12 people including 8 parents and 4 teachers. To choose 6 out of this 12 people, we use the concept of combination.

n = 12C6 = 924

To choose, 3 parents out of the 8 parents, we use again the concept of combination.

x = 8C3 = 56

Similarly, we use the same concept for choosing 3 teachers out of 4 teachers.

y = 4C3 = 4

The probability required in this item can be solved through the equation,

P = xy/n

Substituting,

P = (56)(4) / 924 = 0.2424

Thus, the probability is 24.24%.

Answer 2

Answer with explanation:

→Total Number of People which are in the group =8 parents + 4 Teacher=12 People

→Probability of an Event

`=\frac{\text{Total Favorable Outcome}}{\text{Total Possible Outcome}}`

→Probability of selecting three parents and three teachers

= Selecting 3 parents from 8 Parents +Selecting 3 teacher from 4 teacher

As order of Arrangement is not Important ,so we will use the concept of Combinatorics.

→→ Required Probability

`=\frac{_(3)^(8)\textrm{C}* _(3)^(4)\textrm{C}}{_(6)^(12)\textrm{C}}\\\\=((8!)/(3!* 5!)* (4!)/(3!* 1!))/((12!)/(6!* 6!))\\\\=(56 * 4)/(7* 4 * 3* 11)\\\\=(8)/(33)`