1. Data help

I'm doing some data hwk and i got stuck at these, can anyone go about showing me how to solve these?

1) A Euchre deck has 24 cards: 9's, 10's, jacks, queens, kings, and aces from each of the four suits. If you were to deal out 5 cards from the deck, what is the probability that there would be a 10, jack, queen, king, and ace all from the same suit?

2) How many paths will spell pascal? ...i just realized that this isn't showing up the way i want it to when i post but it goes out like a triangle up to the C and then it closes back like a diamond
P
A A
S S S
C C C C
A A A
L L

I did this and i got 20 but i'm not sure if i'm right

3) A dart board contains 20 equal-sized sectors numbers 1 to 20. A dart is ramdomly tossed at the board 10 times. what is the probability that that dart lands in the sector labled 20 a total of 5 times.

I tried question 3 and i did this, can anyone tell me if i'm right?
(10C5)*[(1/20)^5]*[(19/20)^5)

Thanks

2. Hello, imthatgirl!

1) A Euchre deck has 24 cards: 9's, 10's, J's, Q's, K's, and A's from each of the four suits.
If you were to deal out 5 cards from the deck, what is the probability that
there would be a 10, jack, queen, king, and ace all from the same suit?

There are: .$\displaystyle {24\choose5} \:=\:42,504$ possible hands.

There are exactly 4 Royal Flushes.

Therefore: .$\displaystyle P(\text{Royal Flush}) \;=\;\frac{4}{42.504} \;=\;\frac{1}{10,626}$

2) How many paths will spell PASCAL?
Code:
                  P
/   \
A       A
/   \   /   \
S       S       S
/   \   /   \   /   \
C       C       C       C
\   /   \   /   \   /
A       A       A
\   /    \   /
L        L
I'll let someone else work on this one . . .

3) A dart board contains 20 equal-sized sectors numbers 1 to 20.
A dart is ramdomly tossed at the board 10 times.
What is the probability that that dart lands in sector "20" exactly 5 times?

I tried question 3 and i did this, can anyone tell me if i'm right?
.$\displaystyle {10\choose5}\left(\frac{1}{20}\right)^5\left(\frac {19}{20}\right)^5$ . . . . Yes!