Answer: The chance both cards will be a spade is [tex]\dfrac{1}{17}[/tex] .
Step-by-step explanation:
We know that , in a standard deck , the total number of cards = 52
The number of spades = 13
If a person selected 2 cards,
The total number of combination of selecting 2 cards out of 52 = [tex]^{52}C_2[/tex]
The number of combination of selecting 2 spade cards out of 13 = [tex]^{13}C_2[/tex]
Then , the probability that both cards will be a spade=[tex]\dfrac{^{13}C_2}{^{52}C_2}[/tex]
[tex]\dfrac{\dfrac{13!}{2!11!}}{\dfrac{52!}{2!\times50!}}\ \ [\because\ ^nC_r=\dfrac{n!}{r!(n-r)!}][/tex]
[tex]=\dfrac{13\times12}{51\times52}[/tex]
[tex]=\dfrac{1}{17}[/tex]
Hence, the chance both cards will be a spade is [tex]\dfrac{1}{17}[/tex] .
