In the layout o f an oriented circuit board for an electroni

In the layout o f an oriented circuit board for an electronic product, there are 15 different locations for chips. If 10 different types o f chips are to be placed on the board, how many differentlayouts are possible? If the 10 chips that are placed on the board are the same type, how many different layouts are possible? If the 10 chips that are placed on the board are divided in 6 chips o f the same type (type I) and 4 chips o f another type (Type II), how many different layouts are possible?

Solution

d)

As layouts depend on order, then there are

15P10 = 10897286400 layouts [answer]

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e)

If order does not matter, there are just combinations,

15C10 = 3003 layouts [answer]

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f)

There are 3003 ways to choose the 10 chips.

Then, there are 10!/[6!4!] = 210 ways to group the chips.

Thus, there are 3003*210 = 630630 such layouts. [answer]