In the layout of a printed circuit board for an electronic product, 12 different locations can accommodate chips.

(a) If five different types of chips are to be placed on the board, how many different layouts are possible?

(b) If the five chips that are placed on the board are of the same type, how many different layouts are possible?

a) 244,140,625 different ways

b) 390,625 different ways

Explanation:

a) If there are 5 ways to place a chip on each location, and there are 12 locations overall, we have:

5^12 ways of placing them

This would mean a total of 244,140,625 different ways

b) If five chips are of the same type, we can first find how many ways we can place chips on the remaining 7 locations:

5^7 = 78,125

Next we can multiply this by the number of ways the next 5 chips could be the same:

78,125 * 5 = 390,625 different ways