In the layout of an oriented circuit board for an electronic

In the layout of an oriented circuit board for an electronic product, there are 15 different
locations for chips.

(f) If the 10 chips that are placed on the board are divided in 6 chips of the same type
(type I) and 4 chips of another type (Type II), how many different layouts are
possible?

Solution

out of the 15 locations we can select 10 locations in ¹⁵C₁₀ ways. and then those 10 chips can be arranged in 10! ways. so all possible cases is ¹⁵C₁₀*10!.

out of 10 chips 6 are of type 1 and 4 are of type 2.

so we can select the locations for type 1 chips in ¹⁵C₆ ways and from remaining 9 locations we can select locations for type 2 chips in ⁹C₄ ways. and then they can be arranged in 10!/(6!*4!) ways.

so probability of the specified event is

¹⁵C₆*⁹C₄*10!/(6!*4!)/(¹⁵C₁₀*10!)=0.001446759 [answer]