Respuesta :
The total cards in a deck = 52, out of which 26 are black and 26 are red.
Among these 52 cards, Heart = 13 , Spade = 13 , Club = 13 and Diamond = 14
We will use the combination formula as:
[tex]^nC_r = \frac{n!}{r!(n-r)!}[/tex]
1. Probability that all four cards are hearts
= [tex]\frac{^{13}C_4}{^{52}C_4}[/tex]
= [tex]\frac{13!}{9! 4!} \times \frac{48! 4!}{52!}[/tex]
= [tex]\frac{17160}{6497400}[/tex]
= 0.0026
2. Probability that all four cards are from red suits
=[tex]\frac{^{26}C_4}{^{52}C_4}[/tex]
= [tex]\frac{26!}{22! 4!} \frac{4! 48!}{52!}[/tex]
= 0.055
3. Probability that all four cards are from different suits
= [tex]\frac{^{13}C_1 \times ^{13}C_1 \times ^{13}C_1 \times ^{13}C_1}{^{52}C_4}[/tex]
= [tex]\frac{13 \times 13 \times 13 \times 13}{270725}[/tex]
= 0.105
