A printed circuit board has eight different in which a component can be placed.

Question

A printed circuit board has eight different in which a component can be placed. If different components a to be placed on the board, how many different designs are possible? A printed circuit board has eight different locations in which a component can be placed. If five identical components are to be placed on the board, how many different designs are possible? Consider an experiment in which you select a molded plastic part, such as a connector, and measure its thickness. What is the sample space S If the objective of the analysis is to consider only whether or not a particular part conforms to the manufacturing specifications. If two connectors are selected and measured, and we are only interested in the number of conforming parts in the sample of two connectors. If we consider an experiment in which the thickness is measured until a connector fails to meet the specifications.

Explanation / Answer

Solution

First Question

a) 4 distinct components and 8 locations

The first component can fit into any one of the 8 locations in 8 ways. Then, the second component can fit into any one of the remaining 7 locations in 7 ways; third into any one of the remaining 6 locations in 6 ways; and fourth into any one of the remaining 5 locations in 5 ways.

So, the answer = 8x7x6x5 = 1680 ANSWER

b) Out of 8 locations, 5 can be chosen in 8C5 ways. Once 5 locations are selected, 5 identical components can be fit into them in any order in just 1 way since components are identical. Thus. Total number of possibilities = 8C5 = (8!)/{(5!)x(3!)} = 56 ANSWER

Second Question (on sample space)

a) Since only one connector is checked and interest is on whether it is good (conforms to specification) or defective (does not conform to specification), the sample space is binomial consisting of just two points, namely good, defective.

b) Since two connectors are checked and interest is on the number of good (conforms to specification) connectors, the sample space consists of just three points, namely 0, 1, 2, meaning both are not conforming. Only one is conforming or both are conforming.

c) In this case, the very first unit may be found non-conforming implying the sample space starts with 1 and mathematically the number can go to infinity. But, if we are looking at sampling a definite number, say n, of units to be checked, the number can at worst be n. Sample space is:

S = {x: x is a positive integer, but less than or equal to n}

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