A taxi is shuttling 11 students to a concert. The taxi can hold 4 students.In how many ways can 4 students be chosen for the taxi's second trip

The number of students are
11.

We know that  it is the number of ways of grouping of 4
persons out of 11 persons.Choosing or grouping is different from
arranging.

We can arange 4 persone from 11 on  4 chairs
11P4 ways = 11*10*9*8 ways.The reason is that the number of choices of arranging on the
1st chair is 11 and the number of choices of 2nd person  from the remaining (11-1) = 10
persons is 10, and in this way for the 3rd and 4 th chair the number of choices are  9
and  8.

Now let us pressume  that  in all possible ways it
is x number of different groups in which we can select 4 persons in each group from 11
persons. In any of these  group of 4 persons could be arranged in 4P4 = 4!. Therefore
the total possible number of ways we can arrange  4 persons from 11 persons = x *
4!.

Therefore 11P4 =
x!*4!

Therefore k = 11P4/4! = 11*10*9*8/(4*3*2*1 )= 330
ways.

Therefore the different ways of making  4 person
group to transport is 330 ways.

But the question
is pertaining to the number of  ways of grouping 4 persons out of 7 remaining persons,
as in  the 1st trip  4 persons have already been
transported.

So applying the same rule , we get
:

x = 7P4/4! = 7*6*5*4 /(4*3*2*1) =  35
ways.