Answer:0.5176
Step-by-step explanation:
Given
We need to draw 5 cards out of 52 cards
So no of ways of choosing 5 cards out of 52 is [tex]^{52}C_{5}[/tex]
Now to choose 3 cards of same suit
First we have to choose 1 suit out of 4 which can be done in [tex]^4C_1[/tex] ways
Now choosing 3 out of 13 cards is [tex]^{13}C_3[/tex]
and remaining two cards can be chosen in [tex]^{49}C_2[/tex]
So total no of ways are [tex]=^4C_1\times ^{13}C_3\times ^{49}C_2[/tex]
So probability [tex]=\dfrac{^4C_1\times ^{13}C_3\times ^{49}C_2}{^{52}C_{5}}[/tex]
[tex]P=\dfrac{4\times 26\times 11\times 49\times 24}{2598960}[/tex]
[tex]P=0.5176[/tex]
