 # 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: $\left(5+4\right)+\left(4+4\right)+\left(3+3\right)+\left(7+4\right)=9+8+6+11=34$ possible projects to choose from. I used the sum rule here.
Is this correct?
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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.