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Three of the eleven students in Mrs. Smith's class were chosen to be interviewed about their class project. If they are interviewed in alphabetical order by last name how many ways can three kids be interviewed?

 Jan 28, 2022
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If you know combinatorics, you will see that this is simply 11 choose 3. 

 

For those of you who don't, the formula for choosing a number out of another number is n! / ((n – r)! r!), where n = number of items and c = how many you choose.

 

11 choose 3 = 11! / (11-3)! * 3! = 11! / 8! 3! = 11*10*9 / 3*2*1 = 11*5*3 = 165 ways.

 

(Alphabetical order does not matter here because you could always reorder them to be alphabetical and combinatorics do not count each combination more than one time)

 

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ShockFish

 Jan 30, 2022
edited by ShockFish  Jan 30, 2022

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