Question

In shuffling a pack of 52 playing cards, four arc accidently dropped ; find the chance that the missing cards should be one from each suit.

Answer 1

Since from well-shuffled pack of cards, 4 cards missed out

$\therefore n\left(S\right){=}^{52}{C}_4$

Let E be the event that four missing cards are from each suit

$\therefore n\left(E\right){=}^{13}{C}_1{\times }^{13}{C}_1{\times }^{13}{C}_1{\times }^{13}{C}_1$

$\therefore P\left(E\right)=\frac{{}^{13}{C}_1{\times }^{13}{C}_1{\times }^{13}{C}_1{\times }^{13}{C}_1}{{}^{52}{C}_4}$

$=\frac{13\times 13\times 13\times 13}{\frac{52\times 51\times 50\times 49}{4\times 3\times 2\times 1}}=\frac{2197}{20825}$