Question

Find the number of ways of choosing $4$ cards from a pack of $52$ playing cards when cards are of the same colour.

• A. $29900$
• B. $29925$
• C. $29910$
• D. $29920$

Answer 1

Answer: (A)

$29900$

Answer 2

$4$ red cards can be selected out of $26$ red cards in $^{26}C_{4}$ ways. $4$ black cards can be selected out of $26$ black cards in $^{26 }C_{4}$ ways. Therefore, the required number of ways $=\,^{26}C_{4} + \,^{26}C_{4}$ = $2 \times \frac{26!}{ 4! 22!} = 29900$.