Permutation problem: Seven friends queue up for a buffet....

[chwala]

Homework Statement

solve the problem below;

Relevant Equations

permutation and combination

 

[chwala]

for the first part, not difficult,
we have $7!=5040$
now for the second part, i get a bit confused here ok, i merged the last two fellows and now i have 6 items...
therefore i will have $6C4$× the remaining $3$ can be arranged in 1 way only= $15$ is this the correct approach?...not one of my favorite topics ...

or can i say that, the car can be filled up in this way,
$5C2 ×1$ way only(remaining 3 people), assuming that the two fellows board the 4-vehicle capacity or
$5C4 ×1$way only(2 fellows plus 1 person) , assuming that the two fellows board the vehicle holding 3 occupants...which gives
$10+5=15$

 

[Delta2]

I agree with your solution.