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1. There are 125 juniors at the high school.How many ways can they elect a
president,vice president, and secretary?

2. Determine the number of 4-letter arrangements that can be made using the
word RHOMBUS.

Respuesta :

JeanaShupp

Answer: 1.   1,906,500

 2.   840

Step-by-step explanation:

1. Given: There are 125 juniors at the high school.

Total positions = 3    [president,vice president, and secretary]

Then, Number of ways to elect a  president,vice president, and secretary( which is in order) out of  125 juniors = [tex]^{125}P_{3}=\dfrac{125!}{(125-3)!}[/tex]  [Using permutations]

[tex]=\dfrac{125!}{122!}\\\\=\dfrac{125\times124\times123\times122!!}{122!}\\\\=125\times124\times123\\\\=1906500[/tex]

Hence, Required ways =1906500

(2) Given word : "RHOMBUS"

Total letters= 7

By permutation, the umber of 4-letter arrangements = [tex]^7P_4=\dfrac{7!}{(7-4)!}=\dfrac{7!}{3!}[/tex]

[tex]=\dfrac{7\times6\times5\times4\times3!}{3!}\\\\= 7\times6\times5\times4\\\\=840[/tex]

Hence, required ways = 840

Cetacea

Answer:

1) The number of ways = 1906500.

2) The number of ways = 840.

1) President, vice president, and secretary are 3 different positions.

There are total 125 students.

So we can select them in [tex]125P3=\frac{125!}{\left(125-3\right)!}=1906500[/tex] ways.

2) There are total 7 different letters in RHOMBUS.

We can select 4 different letters from 7 letters in [tex]7P4=\frac{7!}{\left(7-4\right)!}=840[/tex].

Learn more: https://brainly.com/question/13769924

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