Find the probability that when a hand of 7 cards are drawn from the well-shuffled deck of 52 cards, it contains (i) all kings (ii) 3 kings

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To find the probability of drawing certain combinations of cards from a well-shuffled deck of 52 cards, we'll first need to understand the total number of possible outcomes and the number of favorable outcomes for each scenario.

(i) Probability of drawing all kings: There are 4 kings in a standard deck. So, the probability of drawing the first king is 4/52, the second king is 3/51, the third king is 2/50, and the fourth king is 1/49. Therefore, the probability of drawing all kings is:

(4/52) * (3/51) * (2/50) * (1/49)

(ii) Probability of drawing exactly 3 kings: To calculate this, we need to consider the number of ways to choose 3 kings out of 4 and the number of ways to choose the remaining 4 cards from the non-king cards. This can be calculated using combinations.

Number of ways to choose 3 kings out of 4: C(4, 3) = 4 Number of ways to choose 4 non-king cards out of the remaining 48: C(48, 4) = 194580

So, the total number of favorable outcomes is 4 * 194580.

To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes, which is C(52, 7).

Now, let's calculate these probabilities:

(i) Probability of drawing all kings: P(All kings)=452×351×250×149P(All kings)=524×513×502×491

(ii) Probability of drawing exactly 3 kings: P(3 kings)=4×194580C(52,7)P(3 kings)=C(52,7)4×194580

You can use a calculator or programming language to compute the exact values. If you need further assistance with the calculations or concepts, feel free to ask!