1. ## 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

2. 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

3. 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:

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

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.

$\displaystyle 8*7*6*5*4*3 = 20160$

4. Originally Posted by mathceleb
I get 28 UNIQUE combinations.

Permutation and Combination Calculator
Mathceleb, it isn't $\displaystyle 8\choose6$