Arrangement of Items

Arrange 5 boxes (A,B,C,D,E) in as many ways as possible. Each time you may select 3 boxes. How many different ways are there?

Answer: Totally 60 ways. They are:

… AND SO ON…

There may be too many choices to count. But we may do it in a systemic way using a table. This table may also be written as:

1^ST BOX 5 choices	2^ND BOX 4 choices	3^RD BOX 3 choices
A	B	C
		D
		E
	C	B
		D
		E
	D	B
		C
		E
	E	B
		C
		D
B	A	C
		D
		E
	C	A
		D
		E
	D	A
		C
		E
	E	A
		C
		D
C	A	B
		D
		E
	B	A
		D
		E
	D	A
		B
		E
	E	A
		B
		D
D	A	B
		C
		E
	B	A
		C
		E
	C	A
		B
		E
	E	A
		B
		C
E	A	B
		C
		D
	B	A
		C
		D
	C	A
		B
		D
	D	A
		B
		C

FINAL ANSWER:

The 60 choices, listed in a table, are:

1^ST BOX 5 choices	2^ND BOX 4 choices	3^RD BOX 3 choices
A	B	C
A	B	D
A	B	E
A	C	B
A	C	D
A	C	E
A	D	B
A	D	C
A	D	E
A	E	B
A	E	C
A	E	D
B	A	C
B	A	D
B	A	E
B	C	A
B	C	D
B	C	E
B	D	A
B	D	C
B	D	E
B	E	A
B	E	C
B	E	D
C	A	B
C	A	D
C	A	E
C	B	A
C	B	D
C	B	E
C	D	A
C	D	B
C	D	E
C	E	A
C	E	B
C	E	D
D	A	B
D	A	C
D	A	E
D	B	A
D	B	C
D	B	E
D	C	A
D	C	B
D	C	E
D	E	A
D	E	B
D	E	C
E	A	B
E	A	C
E	A	D
E	B	A
E	B	C
E	B	D
E	C	A
E	C	B
E	C	D
E	D	A
E	D	B
E	D	C