Question

You are playing a solitaire game in which you are dealt three cards without replacement from a simplified deck of 10 cards (marked 1 through 10). You win if one of your cards is a 10 or if all of your cards are odd. How many winning hands are there if different orders are different hands?

Answer 1

10*9*8 + 5*4*3 = 780

Answer 2

If the first card drawn is a 10, there are 9P2 permutations of the remaining cards, giving 9 * 8 = 72 hands.
If the second card drawn is a 10, there are 9 possible numbers for the first card and 8 possible numbers for the third card, giving 9 * 8 = 72 hands.
If the third card drawn is a 10, there are 9P2 permutations of the first and second cards, giving 72 hands.

There are five odd numbers giving 5P3 = 5 * 4 * 3 possible hands.

the total possible number of winning hands is 72 + 72 + 72 + 60 = ?

Answer 3

I figured it out Thanks Anyway the answer was 276/720 combined.