Q77 / 160 · AP EAMCET 2022 (08 Jul Shift 1) · Mathematics

Four cards are drawn at random from a pack of 52 playing cards. The probability of getting all four cards of the same suit is

  • A
    $\frac{13}{270725}$
  • B
    $\frac{91}{190}$
  • C
    $\frac{178}{20825}$
  • Correct answer
    D
    $\frac{44}{4165}$

Solution

$\mathrm{P}$ [All your cands are of the same suit] $\begin{aligned} & =\frac{13_{\mathrm{C}_4}+13_{\mathrm{C}_4}+13_{\mathrm{C}_4}+13_{\mathrm{C}_4}}{52_{\mathrm{C}_4}} \\ & =\frac{4.13_{\mathrm{C}_4}}{52_{\mathrm{C}_4}}=\frac{\frac{4.13 .12 .11 .10}{4.8 .2 .1}}{\frac{4.52 .51 .50 .49}{4.3 .2 .1}} \\ & =\frac{12 \times 11}{51 \times 5 \times 49}=\frac{44}{85 \times 49}=\frac{44}{4165}\end{aligned}$

Hence, the correct answer is option: 'D'.

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