A deck of cards in a game contains all four suits (Clubs ♣ and Spades ♠, which are black, and Hearts ♥ and Diamonds ♦, which are red), but only the cards with values 5, 6, 7, 8, 9, and 10.  How many different 5-card hands can be formed that contain at least 4 red cards?  How many different 5-card hands can be formed that contain at least one club and at least one heart?    How many different 5-card hands can be formed that contain at least one spade and at least two 10s?    Would like a proper answer no repeats of past answers, a description of the formula used and explanation as to why everything was done

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