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Three cards are selected from a well-shuffled deck of 52 cards. Find the probability that all 3 are Aces.

Sagot :

Answer:

We can divide the pack of cards in two ways

Non Ace cards and Ace cards

Since there are 4 aces in a pack

No of non ace cards will be 52–4=48

The question mentions atleast 1 ace cards so i can pick 1 ace card,2 ace cards or 3 ace cards

Case1:1 Ace card

1 will pick one ace card and 2 non ace cards

It can be done in 4C1*48*C2 ways

= 4*1128 = 4 512 ways

Case 2: 2 Ace Cards

I will pick 2 ace cards and 1 non ace card

It can be done in 4C2 * 48C1 = 6 * 48 =288 ways

Case 3:3 Ace cards

It can be done in 4C3 =4 ways

Therefore the probability is

(4512+288+4)/52C3

=4804/22100=0.217

Step-by-step explanation:

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