Question

URGENT exam question!! : in a standard deck of 52 cards, determine the number of 5-card hands that must contain at least 3 queens.

I have done this before, but I have forgotten the whole process and my final exam is tomorrow D:

Answer 1

I'm not 100% sure, but from what I remember about probability:
Your desired decks are either 3 queens + 2 (any non-queen card) or 4 queens + 1 (any non-queen card).
We use combinations because the order does not matter. What this means is that we don't care whether we draw a queen of hearts, then spade, then diamond--a queen is a queen.
Translated into English, we can say:
freshfaced wants three queens AND two cards (of any other face) OR four queens AND one card (of any other face).
The "OR" implies addition, the "AND" implies multiplication.
First part:
From a standard deck which has 4 queens, we want 3 queens, and from the remaining 48 non-queen cards, we want 2 cards, which we can write as
part1 = C(4,3) + C(48,2)
Second part:
From a standard deck which has 4 queens, we want 4 queens, and from the remaining 48 non-queen cards, we want 1 card, which we can write as
part2 = C(4,4) + C(48,1)
Now add up the values for 'part1' and 'part2' and that *should* be the number of possible 5-card hands. Please check to make sure it's correct!

Answer 2

@DisplayError Yep I got that ! Thanks!!