Mathematics, 13.10.2019 04:30 kkruvc

Acommittee consisting 4 of faculty members and 5 students is to be formed. every committee position has the same duties and voting rights. there are 9 faculty members and 14 students eligible to serve on the committee. in how many ways can the committee be formed?

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Answer from: madbiebzz

ANSWER:

The committee can be formed by 252252 ways

SOLUTION:

Given, a committee consisting 4 of faculty members and 5 students is to be formed.

There are 9 faculty members and 14 students eligible to serve on the committee.

We need to find In how many ways can the committee be formed.

Every committee position has the same duties and voting rights. So, we need not consider any order and we just need to find the total possible combinations.

Total possible combinations = combinations possible for teachers $\times$ combinations possible for students.

Now, combinations possible for teachers = 4 out of 9 teachers

$\begin{array}{l}{=^{9} \mathrm{C}_{4}} \\\\ {=\frac{9 !}{(9-4) ! 4 !}} \\\\ {=\frac{9 !}{5 ! \times 4 !}} \\\\ {=\frac{9 \times 8 \times 7 \times 6 \times 5 !}{5 ! \times 3 \times 2 \times 1}} \\\\ {=\frac{3024}{24}}\end{array}$

Combinations possible for teachers = 126

Now, combinations possible for students = 5 out of 14 teachers

$\begin{array}{l}{=^{14} \mathrm{C}_{5}} \\\\ {=\frac{14 !}{(14-5) ! 5 !}} \\\\ {=\frac{14 !}{9 ! \times 5 !}} \\\\ {=\frac{14 \times 13 \times 12 \times 11 \times 10}{5 \times 4 \times 3 \times 2 \times 1}} \\\\ {=\frac{240240}{120}}\end{array}$

Combinations possible for students = 2002

Now, Total possible combinations = 126 $\times$ 2002

Total possible combinations = 252252.

Hence, totally 252252 possible ways are there to form the committee.

Answer from: Quest

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

Answer from: Quest

50-38=12

step-by-step explanation:

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