Ministry of Education are inviting tender for four categories promoting the use of IT in education.

Porter Mccullough 2022-05-02 Answered
Ministry of Education are inviting tender for four categories promoting the use of IT in education. Each category consists of 5, 4, 3, and 7 projects, respectively. Each project appears on exactly one category. How many possible projects are there to choose from? Explain your answer.
My Answer: ( 5 + 4 ) + ( 4 + 4 ) + ( 3 + 3 ) + ( 7 + 4 ) = 9 + 8 + 6 + 11 = 34 possible projects to choose from. I used the sum rule here.
Is this correct?
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Answers (1)

Frederick Greer
Answered 2022-05-03 Author has 17 answers
Since each project appears in exactly one category, the four lists of projects can be combined into one list of projects containing 5 + 4 + 3 + 7 = 19 projects. Hence, there are 19 projects from which to choose.
The Addition Principle (or Sum Rule) states that if there are n 1 ways of performing one task and n 2 ways of performing another task that cannot be performed at the same time, there are n 1 + n 2 ways of performing both tasks.
In this case, we can select a project from category one in five ways, a project from category two in four ways, a project from category three in three ways, or a project in category four in seven ways. Since it is not possible to choose the same project from more than one list, the Addition Principle applies. Hence, there is a total of 5 + 4 + 3 + 7 = 19 projects from which to choose.
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