Question

Tania and bob are designing a soccer uniform. They want to use two color on the shirt. Their choices are green, orange, yellow,purple, blue,and silver.How many ways can they choose two color?

Answer 1

The problem isnt very clear about it...but im going to assume that we cant pick the same color twice, is that ok?

Answer 2

yes they can!

Answer 3

so its ok to pick orange and orange? alright lets see...

Answer 4

So for the first color, they have 6 choices, and for the second they also have 6 choices. So the number of combinations is 6*6 = 36. However, if i pick say green and silver, that is the same as picking silver and green. Since each combination can be flipped and not change, i need to divide by 2 to account for that. So the correct answer is 36/2 = 18.

Answer 5

the function joe is describing is called the "choose" function(combination function) i.e. n choose k

Answer 6

its not really the choose function, since we can pick the same color twice. If there was a restriction as to only being able to pick a color once, then it would be 6C2:\[\left(\begin{matrix}6 \\ 2\end{matrix}\right) = \frac{6\cdot5}{1\cdot2} = 15\]

Answer 7

sorry joes' explanation for the choose function is correct ... it only applies to situations without repitition