SOLUTION: A deck of 40 cards contains 10 green cards, 29 blue cards, and 1 red card. The first card you draw is the red card. You draw 6 other cards without replacement. What is the pro

So what you have now is a deck of 39 cards containing 10 
green cards and 29 blue cards.

We use the complement event, and then subtract its probability from 1.

The complement event is to draw 6 non-green cards in a row.

There are 29 non-green cards, so the probability of drawing
a non-green card the first time is .

Now there are 28 non-green cards, so the probability of drawing
a non-green card the second time is .

Now there are 27 non-green cards, so the probability of drawing
a non-green card the third time is .

Now there are 26 non-green cards, so the probability of drawing
a non-green card the fourth time is .

Now there are 25 non-green cards, so the probability of drawing
a non-green card the fifth time is .

Now there are 24 non-green cards, so the probability of drawing
a non-green card the sixth time is .

So the probability of drawing a non-green card each of those
six times is the product of those probabilities



Then 

Edwin