Probability lollipops

P(Orange + Orange) = $\left(\frac{4}{9}\right)\left(\frac{3}{8}\right) = \frac{12}{72}$

P(Green + Green) = $\left(\frac{3}{9}\right)\left(\frac{2}{8}\right) = \frac{6}{72}$

P(Red + Red) = $\left(\frac{2}{9}\right)\left(\frac{1}{8}\right) = \frac{2}{72}$

Probability that the lollipops are the same colour $= P(OO) + P(RR) + P(GG) = \frac{12}{72} + \frac{6}{72} + \frac{2}{72} = \boxed{\frac{20}{72}}$

Ways to choose two orange: $4 \cdot 3 = 12$

Ways to choose two red: $2\cdot 1=2$

Ways to choose two green: $3\cdot 2=6$

Total ways to choose two without restriction: $9\cdot 8=72$

Therefore the total probability is $\frac{12+2+6}{72} = \frac{5}{18}$ But then you notice that the problem maker forgot to put his answer choices in simplest terms (smh problem maker) so we choose the equivalent answer of 20/72.

Using combinations:

We can choose two orange lolipops in $\binom{4}{2}$ ways.

We can choose two red lolipops in $\binom{2}{2}$ ways.

We can choose two green lolipops in $\binom{3}{2}$ ways.

We can choose two lolipops of any color in $\binom{9}{2}$ ways.

Then:

$\frac{\binom{4}{2}+\binom{2}{2}+\binom{3}{2}}{\binom{9}{2}}=\boxed{\frac{20}{72}=\frac{5}{18}}$

So if one, uses Combinations to solve this problem, why would it be 9C1 * 8C1 and not 9C2 in the denominator?

4/9 3/8=12/72
2/9
1/8=02/72 3/9*2/8=06/72 =20/72