How many ways can 3 students be selected from a group of 10 students?

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How to solve a counting problem using permutations and combinations.
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9 июл 2024

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Комментарии : 25

@kahunamaui 11 месяцев назад

You are a great teacher. I actually like you conversational / lecture style. I can see you have experience with helping math challenged students gain confidence. I am seeing some students in k7- k10’that do not know the concept of a decimal verses a fraction or percentage.

@paulpurpura191 11 месяцев назад

Hey John! Here is a permutation problem with a wrinkle. If you choose to solve it, I would like to see your answer. Keep up the great work. I always enjoy your math videos. I do have a solution for this problem. I want to see if I did it right. An archery target has 10 concentric rings that are used for scoring in an archery match. Each ring has it own score value. A hit to the outermost ring scores 1 point. Score values for each subsequent inner ring increase by 1 point. If an archer shoots 6 arrows, how many permutations are possible? Note: 1. If an arrow does not hit a target ring, no points are scored. 2. An arrow can hit the same target ring more than once.

@devonwilson5776 10 месяцев назад

Greetings. Thanks for the happy face. The answer is definitely 120. Determined using combinations. (10x 9x8) ÷ (3x2×1)=5×3×8=120.

@mj3845 10 месяцев назад

This problem is way over my head in terms of math education, but it was fun to listen to. I understood bits of it.

@olivemd 11 месяцев назад

Amazed I still remember this.

@vespa2860 11 месяцев назад

So a combination lock is actually a permutation lock. That clears up everything! In your example you could cross cancel more - leaving 10X3X4 (3 and 2 are removed from the denominator).

@smhwolvi 11 месяцев назад

i was just learning this during my (unfortunate) summer school classes, and suddenly i get this video on my feed when i open youtube. thank you magic math guy

@YADAMNDADDY 9 месяцев назад

Summer school?

@smhwolvi 9 месяцев назад

@@YADAMNDADDY yeah when you fail some classes you have the opportunity to sign up for summer school so that you can get the credit and not be held back a grade to repeat it

@nicholasb8900 6 месяцев назад

Is there an way to use a calculator for partial factorials. For example if you wanted to do the integers from 15-22 what would be the best model to do it besides doing it manually which could be time consuming with more integers?

@henkhu100 8 месяцев назад

The problem is that the question is not quit clear. "how many ways". If you select student 3, then student 4 and then student 6, the way you selecte them is different from selecting nr4, then nr 6 and then nr 1. The result will be the same. The "way of selecting", so the process of selecting them, is different. So there are also arguments for 720 as the correct answer.

@royforgy3219 5 месяцев назад

Love you problems.

@kahunamaui 11 месяцев назад

Is a bicycle three digit combination lock’s possible combinations 10 to the power of three (1,000)? If so, why does not it follow the n p k as demonstrated here.?

@MrMousley 8 месяцев назад

1st student is selected from the full group of 10 the 2nd student is then selected from a group of 9 and the 3rd from a group of 8 Which is 10 x 9 x 8 = 720 combinations ... BUT !! This number would say that ABC and BAC and CBA were different and they aren't ... so we need to divide by 3 x 2 x 1 720/6 = there are only 120 DIFFERENT combinations

@genelowry5666 11 месяцев назад

My answer = 10C3 =120 aka 10X9X8/3!

@user-ri6rn7ti5h 9 месяцев назад

(10÷3)= 3/1 (x+1x-3)

@user-ri6rn7ti5h 9 месяцев назад

(342÷9)= 38(x+3x-8

@tomtke7351 11 месяцев назад

first choice one of ten 2nd one of nine 3rd one of eight thus 10×9×8 = 720 if order is not important 720/3! = 120 i.e. how many ways can 3 elements be arramged? first choice = 3 2nd = 2 3rd = 1 3×2×1 = 6

@larsfladmark2482 11 месяцев назад

I got 720 in my head.

@brianmcguigan4785 11 месяцев назад

I fully understand the maths, but YOU have to be careful about how you describe the problem. Ways of 'picking' implies order, 'selecting' doesn't.

@Dunning_Kruger_Is__On_Youtube 11 месяцев назад

I think the thesaurus would disagree with you on the difference between pick, select, choose. Moreover, can’t you randomly “pick” socks out of a drawer thereby negating any sense of order?

@ckjamn 8 месяцев назад

I said 90 . Immediately Not a wizz

@robertakerman3570 11 месяцев назад

How many "differently"? Not watching today.

@WelshPaulJames 10 месяцев назад

John Dee, really?

@BuiltatBlackjacks 3 месяца назад

Good job you're not an English teacher then. Way implies permutation. Picking 3,2,then 1 is a different way of getting a group of 3 than picking 2,3,then 1.