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

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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.

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.

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 =)!