There are 5 red balls, 5 white balls and 3 green balls in a bag. Nelson is blindfolded before he draws 3 balls from the bag. List out all the possible results for the colors of balls he will draw out from the bag.
To list out the possible results for the colors of balls Nelson will draw, we can use a combination formula. Since Nelson is blindfolded and the order of the balls doesn't matter, we need to find the number of combinations of 3 balls out of the total 13 balls in the bag.
The combination formula is given by:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of balls and r is the number of balls to be drawn.
In this case, n = 13 and r = 3.
C(13, 3) = 13! / (3!(13-3)!)
C(13, 3) = 13! / (3! * 10!)
Now, let's calculate the combination:
13! = 13 * 12 * 11 * 10!
3! = 3 * 2 * 1 = 6
10! = 10 * 9 * 8 * 7 * 6!
Simplifying:
C(13, 3) = (13 * 12 * 11 * 10!) / (6 * 10 * 9 * 8 * 7 * 6)
Cancelling out common factors:
C(13, 3) = 13 * 11 / (8 * 7)
C(13, 3) = 143 / 56
Now, let's calculate the value:
C(13, 3) = 2.55
Since the number of combinations must be a whole number, we can conclude that there are 2 possible results for the colors of balls Nelson will draw from the bag.
There are 3^3 possible choices.
Think of counting in base 3, where R=0 W=1 G=2