Combination/Permutation Math Problem

[silveryhair]

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Can anyone please explain how to calculate this problem?

The Metropolitan museum of art wants to borrow three paintings from a private collection consisting of 6 Kandinskys and 4 Chagalls. In how many ways can these paintings be chosen if at least one of them must be a Kandinsky?

Answer is: 116

Thanks!

 

[TK2006]

Can anyone please explain how to calculate this problem?

The Metropolitan museum of art wants to borrow three paintings from a private collection consisting of 6 Kandinskys and 4 Chagalls. In how many ways can these paintings be chosen if at least one of them must be a Kandinsky?

Answer is: 116

Thanks!

Okay, so we have

6 K's
4 C's

We need combo of three paintings with at least one of them being a K.

so we can have

K C C (case 1), K K C (case 2), and K K K (case 3)

Case 1: 6C1*4C2 = 36
Case 2: 6C2*4C1 = 60
Case 3: 6C3 = 20

36+60+20 = 116.

Hope that helps!

 

[silveryhair]

Awesome!!! Thanks buddy!

 

[TK2006]

No prob! Good luck! If you have any more questions, just shoot me a PM, and I will do my best to help!

 

[LuckMC11]

how would u do nCr quickly in your head to answer this question?

 

[TK2006]

how would u do nCr quickly in your head to answer this question?

Just writing it out and canceling as much as you can. For example, 6C2 will give you 6!/(4!*2!). From here I just cancel 4! completely on top and bottom to obtain (6*5)/(2*1). From here, I cancel the 2 on the bottom to obtain (3*5). Now that just equals 15.

I don't know if that answers your question... It's probably how everybody does it... Anyway, sorry if that didn't help! 😳

 

[TK2006]

And, yeah, this question would take a little longer than most other problems...not by much, though.

 

[LuckMC11]

yes that does! i was getting confused on how to set it up tahts all lol. thanks again!

 

[ScratchMan]

10c3 - 4c3

 

[mustardseed5]

I follow permutations and understand this problem, but what does nCr refer to??

THANKS!

 

[TK2006]

I follow permutations and understand this problem, but what does nCr refer to??

THANKS!

nCr means "n choose r." It's a notation for combination, which is related to permutation.

You have "n" number of items to choose "r" number of items from to make your arrangements.

You can easily google it and see what it means if you are still confused.🙂

 

[MowgliR]

Okay, so we have

6 K's
4 C's

We need combo of three paintings with at least one of them being a K.

so we can have

K C C (case 1), K K C (case 2), and K K K (case 3)

Case 1: 6C1*4C2 = 36
Case 2: 6C2*4C1 = 60
Case 3: 6C3 = 20

36+60+20 = 116.

Hope that helps!

I dont understand what you did here. How did you get 36, 60, 20?