Question

Four cards are drawn at random from a pack of 52 playing cards. find the probability of getting 3 diamond and 1spade

Answer 1

Given deck of 52 cards

Cards have 13 diamond cards and 13 spades

∴∴ Totally 4 cards are to be obtained

⇒⇒ Number of ways selecting 4 cards out of 52 cards

n(S)=52C4

Step 2:

Let E be the event obtaining 3 diamonds and 1 spade

⇒n(E)=13C3×13C1⇒n

∴∴ Required probability =n(E)n(S)n(E)n(S)

⇒13C3×13C1 ÷ 52C4


The property of combination NCr

= n! ÷ r! ( n - r )!