Could someone please explain to me why my idea for answering the following question is not correct:

Suppose a box contains 10 balls of which 3 are red, 4 are white and 3 are green. A sample of 4 balls is selected at random without replacement. Find the probability of the event the sample contains 2 red balls

My process of thinking:
(ball 1) can be red in 3 ways
(ball 2 ) can be red in 2 ways
(ball 3) remaining colours in 7 ways
(ball 4) remaining colours in 6 ways

so desired outcomes can happen in 3x2x7x6 = 252 ways
How mayn possible outcomes in total = 10x9x8x7 = 5040 ways

so P(2 red balls in the set) = 252/5040

However the textbook give us the answer (3C2) * (7C2) / (10C4) = 3/10

Now I have read previous topics that discuss this confusion of when to choose "order matters" and "order does not matter"

https://www.beatthegmat.com/combination- ... t8924.html

Ian Stewart mentions that it does not matter which approach you take so as long as you are consistent in calculating numerator and denominator (ie calculating using permutations OR combinations) the difference should be by a constant .... could someone please clarify what I am doing wrong as I am consistent in my calculation

- Thanks