# In how many ways can 2 balls be drawn from a box containing 7 red and 6 green balls?

2
by ZittyNakahara

2015-12-12T08:45:40+08:00

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This is an example of Combination.
Combination is a number of ways of selecting r items from a set of n.
This can be denoted as nCr = n!/r!(n-r)!

It doesn't specify here what color of the ball we will be drawn from a box and there are total of 13 balls in a box. So, there will 13C2 ways of drawing a ball from a box.
Let's try to solve this.
nCr = n!/r!(n-r)!
13C2 = 13! / 2!(13-2)!
= 13! / 2!(11!)
= (13×12×11!) / (2×1×11!)
= (13×12) / (2×1)
= 156 / 2
13C2 = 78 ways

Therefore, there are 78 ways that  the 2 balls can be drawn from a box containing 7 red and 6 green balls.
2015-12-12T16:53:04+08:00
In statistics, this is called combination wherein order doesn't matter! the formula is:
C=
where:
n=total number of objects
r=number of objects you need
or if you have studied about permutation:
C=
Get the total # of balls:
7+6=13

substitute:
C=
C=
Cancel out the 11! and divide 12 by 2 now you have:
C=13x6
C=78
or just input at the calculator 13C2 and its the same =)
Hope this helps =)!