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- Thread starter micky123
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There are 4 cards (ACE included) with pictures AND heart.From a standard pack of 52 cards, I draw 3 cards at random without replacement. What is the probability that all cards drawn are both hearts and picture cards?

is the answer: (3/52)*(2/51)*(1/50)?

How many ways can you draw 3 cards from that group ?

How many ways can you draw 3 cards from 52 cards ?

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If ACE is not included then - how many ways can you choose 3 cards from that group (Hearts and pictures) ? ------ 1 wayWhy would ace be included? I thought there are only 3 cards that are both heart and picture? (jack, queen and king)

Please kindly explain if I have gotten it wrong! Thank you.

How many ways can you choose 3 cards (no restriction) from the deck? _____ \(\displaystyle C^{52}_{3}\)

Now calculate probability.

reference: https://math.stackexchange.com/ques...-getting-3-cards-in-the-same-suit-from-a-deck

Am I understanding the event incorrectly? I understood the event that “all three cards are both heart and picture” to be drawing “a jack, a queen and a king of hearts”, which is 1 out of 22100 ways.

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I would agree with your first answer [imath]\left(\dfrac{3}{52}\right)\cdot\left(\dfrac{2}{51}\right)\cdot\left(\dfrac{1}{50}\right)[/imath].

Am I understanding the event incorrectly? I understood the event that “all three cards are both heart and picture” to be drawing “a jack, a queen and a king of hearts”, which is 1 out of 22100 ways.

BUT if I were reading this question as an editor I would object to its wording as being unclear. It is extremely unusual to use

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Your wikipedia link states that names 'picture card' and 'face card' mean the same thing.It is extremely unusual to usepicture cardwhat standard English usesface cards.

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Because a lot of card manufacturers draw a picture on each ace. However, the design on the aces do not show a person.confused as to why there are 4 cards with pictures and heart?

The name 'picture card' refers only to cards containing a picture of a person.

if ace is not considered a picture card, the ans would be (3/52)*(2/51)*(1/50).

if ace is considered a picture card, the and would be (4/51)*(3/51)*(2/50).

am i right?