Answer to Question #322786 in Statistics and Probability for Ace Solangon

Question

Two cards are drawn from a deck. How many possible value following variables take? 1. sum of the numbers on the cards 2. number of times both cards are black 3. Number of times both cards are 7s 4. Number of times the first card is six and the second card is red 5. Number of times the first card is face card and the second card is not a face card

Answer 1

1. There are 9 cards with numbers (from 2 to 10), and 4 cards without numbers(from jack to ace) So, the sum of the numbers can be from 2 to 20.
2. There are 26 black cards, so, there are $C_{26}^2=325$ times both cards are black
3. There are 4 sevens, so there are $C_4^2=6$ times both cards are sevens
4. There are 4 6s and 26 red cards, so there are $C_4^1*C_{26}^1=104$ times
5. There are 12 face cards and 39 non-face cards, so there are $C_{12}^1*C_{39}^1=468$ times