The probability of getting different suit cards and different denomination cards when two cards are drawn from a pack is
- $\displaystyle \frac{13}{17}$
- $\displaystyle \frac{13}{34}$
- $\displaystyle \frac{12}{17}$
- $\displaystyle \frac{6}{17}$
Total ways to draw 2 cards from 52 is 52C2 = 1326. Ways to get same suit is 4 * 13C2 = 312. Ways to get same denomination is 13 * 4C2 = 78. Total same suit or same denomination = 312 + 78 = 390. Probability of same = 390/1326 = 5/17. Probability of different = 1 - 5/17 = 12/17.
The sample space for drawing two cards from a pack of 52 is 52C2, which equals 1326. Using the complementary event approach, the probability of getting different suits and different denominations is equal to one minus the probability of getting the same suit or the same denomination. The probability of getting the same suit is 4 times 13C2 divided by 52C2, which is 12/51, and the probability of getting the same denomination is 13 times 4C2 divided by 52C2, which is 3/51. Therefore, the required probability is 1 minus the sum of 12/51 and 3/51, resulting in 36/51 or 12/17.