You select 10 cards randomly from a deck of 52 cards.

What is the probability that all of the cards selected are face cards (i.e. jacks, queens, or kings)?

There are 12 face cards in the deck.

P = 12/52 * 11/51 * 10/50... * 3/43

total number of cards=52

number of face card=12
so the probability of all face card=12/52=3/13

1 what is the probability that the selected card is heart?

2 whar is probability that the selected card is king?

To find the probability of selecting all face cards from a deck of 52 cards when selecting 10 cards randomly, we need to determine the number of desired outcomes and the number of possible outcomes.

Number of desired outcomes:
Out of the 52 cards in a standard deck, there are 12 face cards (4 jacks, 4 queens, and 4 kings). We want to select all 10 face cards, so we can choose any combination of 4 out of the 12 face cards. This is calculated using combinations, denoted by "C". The number of combinations of selecting 4 face cards out of 12 is given by:
C(12, 4) = 12! / (4! * (12-4)!) = 495

Number of possible outcomes:
When selecting 10 cards randomly from a deck of 52 cards, the total number of possible outcomes is given by the number of combinations of selecting 10 cards out of 52, which is:
C(52, 10) = 52! / (10! * (52-10)!) = 8,751,555

Therefore, the probability of selecting all face cards when selecting 10 cards randomly is:

Probability = Number of desired outcomes / Number of possible outcomes
= 495 / 8,751,555
≈ 0.0000565

So, the probability is approximately 0.0000565 or 1 in 17,668.