From a group of three boys and four girls, a line of children ordered

Question

From a group of three boys and four girls, a line of children ordered from left to right is to be selected to salute the flag. If exactly three children are in the line, how many different such lines can be formed?

A. 35
B. 70
C. 105
D. 210
E. 630

A. 35
B. 70
C. 105
D. 210
E. 630

mehrotrayashraj · Answer

I am confused if it is 7*6*5 = 210
Or whether it is 3C7 = 35.

I always get confused in such questions. @Bunnel can you please help?

ishan92 · Answer

We have a total of 7 children(3B+4G).
Suppose this is the line _ _ _
We have 3 positions, 
For the first position, we have 7 options
For the second position, we have 6 options
For the third position, we have 5 options

Therefore, total arrangements= 7*6*5=210

JeffTargetTestPrep · Answer

We need to determine the number of ways we can arrange 3 children from 7. Since order is important, we will use permutations.

7P3 = 7!/(7-3)! = 7!/4! = 7 x 6 x 5 = 210

Answer: D

albinaluckyone · Answer

How do you guys know that the order is important in his case? I was taught that there will be signs like words "Title etc" but here we have to simply pice 3 people out of 7 - i have know idea how to differenciate one Permutations from combinactions especially in thi case

MuditKapoor · Answer

People are distinct in every factor unlike they are completely alike or mentioned in the question. 
Just like ABCD alphabets are different.
Also in this question suppose RAJ standing ahead of Nidhi will be different form Nidhi standing ahead of RAJ, hence we will be taking these as 2 different scenarios.

napolean92728 · Answer

first you pick 3 students in 35 ways and then arrange them in 3! ways that gives 35 * 6 = 210 as the answer, Or what you can do is directly arrange 3 students from 7 using 7P3 formula and voila you get the answer, hope you get it .

AvaneeshT · Answer

Hi,
As the question mentions that the order is Important, 210 will be the answer.

From a group of three boys and four girls, a line of children ordered

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From a group of three boys and four girls, a line of children ordered

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