Hello, risteek!

Strange wording . . . the "at least" is unnecessary.You are dealing from a standard deck of cards,

a) How many 4-card hands have at least one card from each suit?

We must have one card from each suit.

There are: 13 choices for the Club, 13 choices for the Heart,

. . 13 choices for the Spade, and 13 choices for the Diamond.

There are: . possible hands.

There are 13 Spades and 39 Others.b) How many 5-card hands have at least one spade?

There are: . possible 5-card hands.

How many haveSpades?no

Then the five cards must be chosen from the 39 Other cards.

There are: . ways.

There are: . hands with at least one Spade.

There are 12 Face cards and 40 Others.c) How many 5-card hands have at least 2 face cards?

The opposite of "at least 2 face cards" is "0 or 1 face card."

0 Face cards

The 5 cards are chosen from the 40 Others.

There are: . ways to get 0 Face cards.

1 Face card

There are: . ways to get one Face card.

There are: . to get 4 Others.

. . There are: . ways to get one Face card.

Hence, there are: . ways to get 0 or 1 Face card.

Therefore, there are: . hands with at least 2 Face cards.