Question

1. There are 125 juniors at the high school.How many ways can they elect a

Answer 1

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 = $^{125}P_{3}=\dfrac{125!}{(125-3)!}$  [Using permutations]

$=\dfrac{125!}{122!}\\\\=\dfrac{125\times124\times123\times122!!}{122!}\\\\=125\times124\times123\\\\=1906500$

Hence, Required ways =1906500

(2) Given word : "RHOMBUS"

Total letters= 7

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

$=\dfrac{7\times6\times5\times4\times3!}{3!}\\\\= 7\times6\times5\times4\\\\=840$

Hence, required ways = 840