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From a pack of 52 cards 3 cards are drawn one by one without replacements.Find the probability that both of them are king ?
- a)132/1338
- b)32/2340
- c)1/5525
- d)4/2755
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
From a pack of 52 cards 3 cards are drawn one by one without replaceme...
4/52*3/51*2/50 = 24/132600 = 4/22100 = 1/5525
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From a pack of 52 cards 3 cards are drawn one by one without replaceme...
Problem: From a pack of 52 cards, 3 cards are drawn one by one without replacements. Find the probability that both of them are king?
Solution:
Total number of ways of drawing 3 cards out of 52 without replacement is:
52C3 = (52 * 51 * 50) / (3 * 2 * 1) = 22100
Let's find out the number of ways of drawing 2 kings out of 4 kings:
4C2 = (4 * 3) / (2 * 1) = 6
Number of ways of drawing the third card which is not a king from the remaining 50 cards is:
48C1 = 48
Therefore, the total number of ways of drawing 2 kings and 1 non-king is:
6 * 48 = 288
So, the probability of drawing 2 kings is:
P = 6 * 48 / 22100 = 1 / 5525
Hence, the correct option is (c) 1/5525.
Solution:
Total number of ways of drawing 3 cards out of 52 without replacement is:
52C3 = (52 * 51 * 50) / (3 * 2 * 1) = 22100
Let's find out the number of ways of drawing 2 kings out of 4 kings:
4C2 = (4 * 3) / (2 * 1) = 6
Number of ways of drawing the third card which is not a king from the remaining 50 cards is:
48C1 = 48
Therefore, the total number of ways of drawing 2 kings and 1 non-king is:
6 * 48 = 288
So, the probability of drawing 2 kings is:
P = 6 * 48 / 22100 = 1 / 5525
Hence, the correct option is (c) 1/5525.
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