Question

From a pack of 52 cards, 3 cards are selected at random. What is the probability of getting more number of kings than queens?

Answer 1

P (K > Q) = P(3K) + P(2K 1Q) = (4/52)(3/51)(2/50)(3!) + (4/52)(3/51)(4/50)(3!)
P (K > Q) = (4/52)(3/51)(6/50)(3!) = 432/132600 (simplify fraction)

Answer 2

The 3! is to say that the order that the cards are taken don't matter.

Answer 3

q for queen , k for king

0 q 1 k
0 q 2 k
0 q 3 k
1 q 2 k
1 q 3 k

so 5 out of the whole space

Answer 4

Wait I forgot to consider the cases for the first 2. Sorry

Answer 5

P (K > Q) = P(3K) + P(2K 1Q) + P(1K) + P(2K)
P (K > Q) = (4/52)(3/51)(2/50)(3!) + (4/52)(3/51)(4/50)(3!) + (4/52)(44/51)(43/50)(3!) + (4/52)(3/51)(44/50)(3!) = 8528/132600 (simplify)

Answer 6

why 3!

Answer 7

@phi

Answer 8

@ganeshie8

Answer 9

@KingGeorge @TuringTest

Answer 10

The 3! represents the number of ways to arrange the 3 cards. When multiplied to the probability it means that the order of which the cards are picked does not matter