A lawn care company has five employees that it schedules on a given da

Question

A lawn care company has five employees that it schedules on a given day to work the lawns of any ten possible homes. How many different ways can the company assign the five employees to the ten homes if each employee provides lawn care service for just one home?

(A) 50
(B) 2
(C) 120
(D) 10!/5!
(E) 10!
IMO:D as 10c1*9c1*8c1*7c1*6c1

(A) 50
(B) 2
(C) 120
(D) 10!/5!
(E) 10!

Ana4001 · Answer

A lawn care company has five employees that it schedules on a given day to work the lawns of any ten possible homes. How many different ways can the company assign the five employees to the ten homes if each employee provides lawn care service for just one home?

(A) 50
(B) 2
(C) 120
(D) 10!/5!
(E) 10!
IMO:D as 10c1*9c1*8c1*7c1*6c1

(A) 50
(B) 2
(C) 120
(D) 10!/5!
(E) 10! 
IMO:D as 10c1*9c1*8c1*7c1*6c1

MartyTargetTestPrep · Answer

Key in answering permutations and combinations questions is creating an accurate mathematical representation of the scenario presented.

To answer this question, we could represent the scenario in a few different ways. One way of representing the scenario is to use two layers of choice.

Since the five workers can work on 5 of the 10 lawns on a given day, the first layer of choice is determining which of the five lawns they will work on that day.

Since they will work on 5 out of 10 lawns, we need to choose 5 lawns.

So the first layer is 10C5 = 10!/5!5!.

Once we have chosen 5 lawns, we arrange the 5 workers on the five lawns.

So we have 5P5 = 5!.

To find the total number of arrangements, we multiply the formulas for the two layers.

10!/5!5! x 5! = 10!/5!

The correct answer is (D).

guhancr7 · Answer

IT IS A PERMUTATION PROBLEM. HOW MANY WAYS 5 PEOPLE CAN BE ASSIGNED TO 10 HOMES. YOU HAVE BEEN ASKED TO ARRANGE THOSE 5 PEOPLE SO ITS 10P5= 10!/5!( derived from the formula nPr= n!/(n-r)!)

You can also solve this problem by using the normal arrangement method.

The first dude can work on any of the 10 lawns , the second has 9 choices since the first has taken one for him. Similarly, the third, fourth and fifth dude has 8, 7 and 6 choices of lawns to choose from. So the different ways the company can assign work to these 5 employees are 10*9*8*7*6 = 10!/5!

ANS D is the right answer choice

Paras96 · Answer

A lawn care company has five employees that it schedules on a given day to work the lawns of any ten possible homes. How many different ways can the company assign the five employees to the ten homes if each employee provides lawn care service for just one home?
Sol=> Firstly we will select 5 out of the ten lawns and since every employee works only on one lawn we will distribute the workers to the five lawns so the number of ways in which this process can be done is---
(10C5) * 5! = (10!/5!5!)*5! = 10!/5!
Hence  option D

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A lawn care company has five employees that it schedules on a given da

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