Six students are to be seated in a row of 6 chairs. if three of thses students must be seated together, how many ways could this be accomplished?

For an instance, A,B,C,D,E,F represent the students, and ABC must be seated together.
Use factorial of 4 (4!). Why 4? Because we have 4 different positions. ABC together, and D, E, F who can be seated separately.
4! = 4 × 3 × 2 × 1
4! = 24

After that, multiply the result of the factorial above by 6. Why 6? Because ABC could have different order: ABC, ACB, BAC, BCA, CAB, CBA, as long as they are together. Therefore,
number of ways = 24 × 6
number of ways = 144

There are 144 ways

Students : A B C D E F
3 of them (A, B, & C) must be seated together

options::
A B C  D E F D E F  A B C D  A B C  E F D E  A B C  F
A B C  D F E D F E  A B C D  A B C  F E D F  A B C  E
A B C  E F D E F D  A B C E  A B C  F D E F  A B C  D
A B C  E D F E D F  A B C E  A B C  D F E D  A B C  F
A B C  F E D F E D  A B C F  A B C  E D F E  A B C  D
A B C  F D E F D E  A B C F  A B C  D E F D  A B C  E

24 options