Whoa, this problem looks a bit tricky...

Let's start with what we know, very card can be a:

red

green

blue

yellow

And each card has a number:

1

2

3

4

5

6

7

We also know that we should be finding probability which would be in the form of:

**successes/total.**

We should start by finding the total number of cards:

There are 4 options for the colors, and 7 options for the numbers so:

4 * 7

= 28 cards in the deck

Then, we are going to be drawing 5, and of the 5, 3 of them have to include the same number.

We can pick the number that all three have in 7 ways,

Then, we can pick choose 3 of the 4 for our different colors,

So, we have

7 * C(4,3) = ?

7 * 4 = ?

28 ways, now we have to pick the other two cards...

Since there are going to be 25 cards left, we have

28 * 25

Then since we are going to be picking another one out of the 24 that are left:

28 * 25 * 24

Now let's find the total number of ways that you can draw 5 cards:

28 * 27 * 26 * 25 * 24

So our probability is:

(28 * 25 * 24)/ (28 * 27 * 26 * 25 * 24)

Simplifying we get:

1/(27 * 26)

= 1/702

So the probability is 1/702 that you get the same number 3 times out of 5.

(If anyone can back me up or reject my answer completely that would be great. I also advise you to read my answer, because I might have made a mistake somewhere ;)