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Title screen: Apply counting principles with Permut and Combin. Copyright ©2017 McGraw-Hill Education. All rights reserved.
Narrator: "In this video, I'll demonstrate how to use the Permutation and Combination formulas in Excel. In this data set, we have the entire diamond inventory of a jeweler. If the jeweler wants to randomly select four diamonds to set up a display in the front window, the order of the diamonds selected will matter, because each permutation, or arrangement of four diamonds, will require a modification to the display. Assume that four of the diamonds will be selected at random. How many possible permutations of four randomly-drawn diamonds are possible? If we solved it by hand, or, rather, by calculator—this is doable—we would use this formula and crunch through some factorials."
The formula: subscript n baseline P subscript r baseline equals start fraction n exclamation point over left parenthesis n minus r right parenthesis exclamation point end fraction.
Narrator: "No big deal. However, Excel will do the work for us with a formula called PERMUT. Let's take a look at the formula. =PERMUT."
Equals PERMUT left parenthesis right parenthesis is entered to cell I7, below subscript n baseline P subscript r baseline in cell I6.
Narrator: "And when I click open parenthesis, I can then click the F(x) button, and the dialogue box will open. Number is the 'N' I have right here, the number that's in inventory in this case. And 'R' is the number chosen. How many of the inventory will I select? If there were only four diamonds, and all four would therefore have to be selected but the order does matter, how many permutations of those four diamonds are there? The answer is 24. If I put 4 here and 4 chosen, you can see the answer comes up already as 24."
Within the Function Arguments dialog box, four is entered to the Number and Number chosen fields. Below the fields, equals 24 is displayed.
Narrator: "But we have 33 diamonds, so we would expect a much larger number of permutations. Let's see what happens."
Thirty-three is entered into the Number field.
Narrator: "982,000, almost 1 million permutations. Of course, in the real world, it is more likely that the jeweler would not pick randomly, but this example does illustrate how many possible outcomes there are when the order matters. The Combination formula, COMBIN, looks very similar. Let's go ahead and open the dialogue box. =COMBIN(, and then click the F(x) to see the dialogue box."
Equals COMBIN left parenthesis is entered to cell I14. The F x button, found left of the formula bar above the sheet, is selected to open the Function Arguments dialog box. A closing parenthesis is automatically applied to the formula.
Narrator: "The difference is in the denominator in this formula."
The formula: subscript n baseline C subscript r baseline equals start fraction n exclamation point over r exclamation point right parenthesis n minus r right parenthesis exclamation point end fraction.
Narrator: "Because the denominator has an extra component, we can expect our result using the same numbers to be smaller. Let's check it with the example of four diamonds and all four being drawn. We use this formula when the order does not matter, only that we have four. So, if we have 4 in inventory and we're going to select 4 and the order doesn't matter, you can guess already that we should have one combination. Let's put that in here. 4 and 4. And as you can see, we have one possible combination. In this example, if we want to know how many combinations of four diamonds are possible, and we don't care about the ordering, only that a diamond has been selected, it turns out that there are about 41,000 combinations."
Thirty-three is entered into the number field to list 40,920.
Narrator: "The difference between permutations and combinations comes down to whether you care about how the items are ordered. If the order matters, then use the permutation formula. If the order doesn't matter, use the combination formula. This video demonstrated how to apply the principles of counting using the PERMUT and COMBIN formulas in Excel."
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Described transcript ©2023 McGraw Hill. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill.
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