If a quality control check is made inspecting a sample of 2

Question

If a quality control check is made inspecting a sample of 2 light bulbs from a box of 12 lighbulbs, how many different samples can be chosen?

A) 6
B) 24
C) 36
D) 66
E) 72

I understand picking 12 options for the 1st light bulb and 11 for the next light bulb but why do you divide this number in half (and how do you know to divide this in half and this will gurantee that all the samples are different?) Thanks

wshaffer · Accepted Answer

Try using the formula for combinations:

n!/r!(n-r)!

12!/2!(12-2)!

12!/2!*10!

12*11/2*1

=66

rlitagmatstudy · Answer

Is there a different way of solving this problem without combinations? Can it be solved with test the answers?

daviddaviddavid · Answer

https://www.khanacademy.org/math/precal ... mbinations go for it

JeffTargetTestPrep · Answer

The number of samples that can be chosen is:

12C2 = 12!/(2! x 10!) = (12 x 11)/2! = 66

Answer: D

alk27 · Answer

Just solved this correctly using a method I learned from a thursdays with ron video ( I think it was from 2017).
Granted, it is not timely, but it worked.

1. List bulbs out from option A - L (1-12)
2. List options that occur once
3. Sum to total

Ex:

A B
A C
A D 
A E
A F
A G
A H
A I
A J
A K
A L

then
BC 
BD
BE..BF.....BL

CD.....CL

You slowly get less and less because the combination already occurs, so you dont count it (eg., LC doesnt count, you already counted CL). Sums to 66.

rahulgoel007 · Answer

We are to choose 2 objects out of the 12 given. Since it is selection, nCr = n!/r!(n-r)!

Here, n=12 and r=2. Substituting, we have

12C2=12!/2!(12-2)!

=12!/2!*10!

=12*11/2*1

=66

So, the answer is D.

crashcarson · Answer

Where do you get the 11 from?

hykhan · Answer

The combinatorial formula is

The total number of units factorial (in this case 12!) divided by (total units - number of choices which in this case is 12-10) factorial times the number of choices factorial. Therefore

12! = 12x11x10x9x8x7...
divided by 
(12-2)! = 10! = 10x9x8x7... times 2!

the 10! cancels out all the values from 10 down in the numerator, hence you're left with 12 x 11 which is divided by 2! (which is 2 x 1) and gives you a value of 66

hope this helps

Hoozan · Answer

It would be much better to use 12C2 and get the answer quickly. But yes, the above method is the logic as to what is exactly going on in this question. I was about to post a similar solution until I saw this

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