# combinations

• May 21st 2008, 08:54 AM
EooD
combinations

1.Private automobile license plates contain three letters followed by three numbers. One example is CCG550. If there are no other constraints, the number of plates that could be manufactured is
A) 150000
B) 17576000
C) 12626000
D) 11232000

2. There are 8 photographs of wildlife to be hung in a display area. The area only has room for 6 photographs at a time. How many different combinations of the photographs are possible?

A) 40320
B) 20160
C) 6720
D) 720

• May 21st 2008, 09:04 AM
mathceleb
Quote:

Originally Posted by EooD

2. There are 8 photographs of wildlife to be hung in a display area. The area only has room for 6 photographs at a time. How many different combinations of the photographs are possible?

A) 40320
B) 20160
C) 6720
D) 720

Permutation and Combination Calculator
• May 21st 2008, 09:06 AM
colby2152
Quote:

Originally Posted by EooD

1.Private automobile license plates contain three letters followed by three numbers. One example is CCG550. If there are no other constraints, the number of plates that could be manufactured is
A) 150000
B) 17576000
C) 12626000
D) 11232000

There are 26 letters in the Latin alphabet. This gives us 26 possibilities for one of the first three slots. There are also 10 digits, so:

\$\displaystyle 26*26*26*10*10*10 = 26^3 * 10^3 \Rightarrow 260^3 = 17576000\$

Quote:

Originally Posted by EooD
2. There are 8 photographs of wildlife to be hung in a display area. The area only has room for 6 photographs at a time. How many different combinations of the photographs are possible?

A) 40320
B) 20160
C) 6720
D) 720

Say one slot can take on 8 photographs. The next slot, given the first slot is filled, can now take 7 photographs. This continues on until the last slot which can take 3 photographs.

\$\displaystyle 8*7*6*5*4*3 = 20160\$
• May 21st 2008, 09:07 AM
colby2152
Quote:

Originally Posted by mathceleb
I get 28 UNIQUE combinations.

Permutation and Combination Calculator

Mathceleb, it isn't \$\displaystyle 8\choose6\$
• May 21st 2008, 09:09 AM
EooD