Hello, Ari!

The Euchre deck is A ,K, Q, J, 10, 9 in four suits,

and 5 cards are dealt to each player.

There are 24 cards in a Euchre deck.

There are: .

(a) What is the probability of being dealt no Jacks?

There are 4 Jacks and 20 Others.

We want 5 Others: .

Therefore: .

(b) What is the probability of being dealt at least 1 Jack?

This is the exact opposite of (a).

Therefore: .

(c) What is the probability of being dealt at least 1 Jack and 1 Ace?

This one requires some Olympic-level gymnastics.

We use this formula:

From (a): .

. . .Then: .

From (d): .

We have: .

This is the exact opposite of "at least one Jack and at least one Ace".

Therefore:

. .

(d) What is the probability of being dealt neither Jacks nor Aces?

There are: 4 Jacks, 4 Aces, and 16 Others.

We want 5 Others: .

Therefore: .

This is getting too long . . . *yawn*

I'll let someone else explain part (e)