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