Question

In a deck of 52 cards, how many ways are there to select 13 Spade and 13 heart cards without repetition

Answer 1

hope this will help u

Answer 2

Answer:

$6.4313598504\times10^{11}$

Step-by-step explanation:

Given : In a deck of 52 cards.

To find : How many ways are there to select 13 Spade and 13 heart cards without repetition?

Solution :

Total number of cards = 52 cards.

To select 13 spade and 13 hearts.

The ways in which they are selecting spade out of 52 is$^{52}C_{13}$

remaining cards = 52-13=39

The ways in which they are selecting heart out of 52 is$^{51}C_{13}$

Solving the combination,

$=^{52}C_{13}+^{39}C_{13}$

$=\frac{52!}{13!39!}+\frac{39!}{13!26!}$

$=6.350135596\times10^{11}+8.122425444\times10^9$

$=6.4313598504\times10^{11}$