ame: Sale h husen CLOSED BOOK, CLOSED NOTES 1- Answer ALL questions. 2- Marks of

Question

ame: Sale h husen CLOSED BOOK, CLOSED NOTES 1- Answer ALL questions. 2- Marks of the examination's questions: es: Question # Mark 4 12 Total 60 15 18 Question #1: In the layout of a printed circuit board for an electronic product, there are 15 different locations that can accommodate chips. (a) If 5 different types of chips are to be placed on the board, how many different layouts are possible? (b) If 5 similar types of chips are to be placed on the board, how many different layouts are possible? Note: both points (a) and (b) have the same mark Answer

Explanation / Answer

(a) Since there are 15 locations and 5 different chips, they can be arranged in

15P5 ways

= 15! / (15-5)!

= 15! / 10!

= 15 * 14 * 13 * 12 * 11 * 10! / 10!

= 15 * 14 * 13 * 12 * 11

= 360360.

(b) Since the chips are similar, we only need to choose them, the order does not matter.

This can be done in 15C5 ways.

= 15! / [(15-5)!5!]

= (15 * 14 * 13 * 12 * 11 * 10!) / (10! 5!)

= (15 * 14 * 13 * 12 * 11) / (5 * 4 * 3 * 2 * 1)

= 3003.

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