probability that exactly two envelopes will contain a card with a matching color Suppose that 10 cards, of which 5 are red and 5 are green, are placed at random in 10 envelopes, of which 5 are red and 5 are green. Determine the probability that exactly two envelopes will contain a card with a matching color.
clearly $\Omega= 10!$
if  I have $ 5c1$  ways red and $5c1$  ways green,  How do I get other permutations?  some hints please

The probability would be 1/5 
only 1 way you can put exactly 2 card in 2 envelope - 1 red card in red envelope and 1 green card in green envelope.
Now, we will need to figure out how many ways cards can be put in the envelope .
you can have - ( considering only one side - lets say red stack)


*

*1 red + 4 green

*2 red + 3 green

*3 red + 2 green

*4 red + 1 green


and lastly,


*

*5 red + 0 green.

