4 cards are drawn from a standard deck of 52 cards. The probability of drawing exactly 2 cards of the same suit is: Option 1: ((^26C_2)(^26C_2))/(^52C_4) Option 2: ((^13C_2)(^39C_2))/(^52C_4) x 3 Option 3: ((^13C_2)(^39C_2))/(^52C_4) x 4 Option 4: ((^26C_2)(^26C_2))/(^52C_4) x 3

Answer: ((^13C_2)(^39C_2))/(^52C_4) x 4. Solution: Choose the suit that contributes two cards in 4 ways, pick 2 of its 13 cards in 132 ways, and take the remaining 2 cards from the other 39. Dividing by 524 gives 4 132392/524.

Algebra

Probability

Medium

core

4 cards are drawn from a standard deck of 52 cards. The probability of drawing exactly 2 cards of the same suit is:

$\frac{(^{26}C_2)(^{26}C_2)}{^{52}C_4}$

$\frac{(^{13}C_2)(^{39}C_2)}{^{52}C_4} \times 3$

$\frac{(^{13}C_2)(^{39}C_2)}{^{52}C_4} \times 4$

$\frac{(^{26}C_2)(^{26}C_2)}{^{52}C_4} \times 3$

✅ Correct Option: 3

Choose the suit that contributes two cards in 4 ways, pick 2 of its 13 cards in $\binom{13}{2}$ ways, and take the remaining 2 cards from the other 39. Dividing by $\binom{52}{4}$ gives $4\,\binom{13}{2}\binom{39}{2}/\binom{52}{4}$ .

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