List all size $4$ subsets from the set $\{A,B,C,D,E,F\}$ List all size $4$ subsets from the set $\{A,B,C,D,E,F\}$
So first I realized this is a permutation because subsets are the same off they have the same elements. So to figure out how many subsets there would be 6p4 which is 15. However I am having trouble listing the actual subsets. Is there a more organized way to go about this so I can ensure I’m not missing any? This is what I have so far: 
$\{A,B,C,D\}
\{B,C,D,E\}
\{C,D,E,F\}
\{D,E,F,A\}
\{E,F,A,B\}
\{F,A,B,C\}
\{B,C,D,F\}
\{A,B,E,F\}
\{A,B,D,F\}
\{C,D,A,F\}$

We need to use "combinations", not permutations.
So we need to use "6 choose 4", or  $\dbinom 64 = \dfrac{6!}{4!2!} = \dfrac{6\cdot 5}{2} = 15$ such subsets (combinations) of $\{A, B, C, D, E, F\}$
Start with all four element subsets starting with $A$:
ABC... (3) $\quad \{A, B, C, D\},\;\;\{A, B, C, E\}, \;\;\{A, B, C, F\}$
ABD..  (2)  $\quad \{A, B, D, E\}, \;\;\{A, B, D, F\}$
ABEF  
ACD... (2)  $\quad \{A, C, D, E\},\;\; \{A, C, D, F\}$
ACEF
ADEF
BCD... (2)  $\quad \{B, C, D, E\}, \;\; \{B, C, D, F\}$
BCEF
BDEF,
CDEF
$$\{A, B, C, D\}, \{A, B, C, E\}, \{A, B, C, F\}, \{A, B, D , E\},$$
$$ \{ A, B, D, F\}, \{A, B, E, F\}, \{A, C, D, E\}, \{A, C, D, F\}, $$ 
$$\{A, C, E, F\}, \{A, D, E, F\}, \{B, C, D, E\}, \{B, C, D, F\},$$ $$ \{B, C, E, F\}, \{B, D, E, F\}, \{C, D, E, F\}$$
