Question

In shuffling a pack of cards; four are accidently dropped; find the chance that the missing cards should be one from each suit.

• A. $1-\frac{{\left(13\right)}^4}{{}^{52}{C}_4}$
• B. $\frac{{\left(13\right)}^4}{{}^{52}{C}_4}$
• C. $\frac{{\left(12\right)}^4}{{}^{52}{C}_4}$
• D. none of these

Answer 1

The correct option is B $\frac{{\left(13\right)}^4}{{}^{52}{C}_4}$

Number of ways of selecting 4 cards from a pack of 52 cards is ${}^{52}{C}_4$
One card from each suit may be dropped in ${}^{13}{C}_1{\times }^{13}{C}_1{\times }^{13}{C}_1{\times }^{13}{C}_1={\left({}^{13}{C}_1\right)}^4$ ways
$\therefore$ Required probability $=\frac{{\left(13\right)}^4}{{}^{52}{C}_4}.$