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# Permutations, combinations, and the multiplication principle for counting

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A committee consisting of 2 faculty members and 3 students is to be formed. Every committee position has the same duties and voting rights. There are 9 faculty members and 12 students eligible to serve on the committee. In how many ways can the committee be formed?

omarsjan  Oct 23, 2018

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Serial numbers for a product are to be made using 3 letters followed by 3 digits. The letters are to be taken from the first 7 letters of the alphabet, with no repeats. The digits are taken from the 10  digits 0, 1, 2, ..., 9, with no repeats. how many serial numbers can be generated?

omarsjan  Oct 23, 2018
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$$n = \dbinom{9}{2}\dbinom{12}{3} = 7920$$

Rom  Oct 23, 2018
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Serial numbers for a product are to be made using 3 letters followed by 3 digits. The letters are to be taken from the first 7 letters of the alphabet, with no repeats. The digits are taken from the 10  digits 0, 1, 2, ..., 9, with no repeats. how many serial numbers can be generated?

omarsjan  Oct 23, 2018
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$$\binom73\cdot\binom{10}3 \Rightarrow 35\cdot720 \Rightarrow25200$$

Guest Oct 24, 2018