Question

Four cards are drawn at random from pack of 52 cards . find probability of getting all four cards of the same number.

Answer 1

Total No. Of cards =52

No.Of cards for each suit = 13

Total types Of French suit = 4(hearts,spades, diamonds,clubs)

Prob. = Conditional case /total case

For this conditional case of selecting all four same suit,it can be either hearts or spades or clubs or diamonds

So Total no. Of conditional case= no. of case of selecting all four cards of hearts suit +no.of case of selecting all four cards of spades suit +no.of case of selecting all four cards of clubs suit + no. of case of selecting all four cards of diamonds suit.

= 13C4+13C4+13C4+ 13C4

=4*(13C4)=2860

Total no. of case= 52C4=270725

So, probability of getting all four cards of the same suit=2860/270725