Question

In shuffling a pack of cards $3$ are accidently dropped, then the chance that missing card should be of different suits is

• A. $169/425$
• B. $261/425$
• C. $104/425$
• D. $425/169$

Answer 1

Answer: (A)

$169/425$

Total number of possibilities for the 3 cards = ${}_3^{52}C$

There are 4 suits with 13 cards each in a deck of 52 cards.

For the 3 missing cards to be different from different suits,

3 out of 4 suits are to be chosen first and then one card out of the selected 3 suits .

So, Number of ways possible=${(}_3^{4}C).{{(}_1^{13}C)}^3$

The chance that missing cards are of different suits

$=\frac{\mathrm{4.13.13.6}}{\mathrm{52.51.50}}=\frac{169}{425}$