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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.

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Yna9141
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 with explanation:

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

→Probability of an Event

                            [tex]=\frac{\text{Total Favorable Outcome}}{\text{Total Possible Outcome}}[/tex]

→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

 [tex]=\frac{_{3}^{8}\textrm{C}\times _{3}^{4}\textrm{C}}{_{6}^{12}\textrm{C}}\\\\=\frac{\frac{8!}{3!\times 5!}\times \frac{4!}{3!\times 1!}}{\frac{12!}{6!\times 6!}}\\\\=\frac{56 \times 4}{7\times 4 \times 3\times 11}\\\\=\frac{8}{33}[/tex]

                                           

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