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

using $10!$ for total number of permutations, imagine that envelopes 1 to 5 are red and 6 to 10 are green, label the cards $R_1$ to $R_5$ and $G_1$ to $G_5$. Then each equiprobable permutation can be written as a 10-tuple.
e.g. $( G_2, G_5, R_1, G_4, G_1; R_2, G_3, R_3, R_4, R_5 )$ has $R_1$ in the third red envelope and $G_3$ in the second green envelope.
In the first 5 red envelopes... 
choose the red card - 5 ways
choose the 4 green cards - 5 ways 
permute the 5 cards - 5! ways
for each way of doing this, the remaining 5 cards can be permuted 5! ways in the 5 green envelopes.
total permutations = $ 5 \times 5 \times 5! \times 5! $
$$ \text{ probability } = \frac {25(5!)^2}{10!} = \frac{25}{252} $$
