The face cards are removed from a full pack. Out of the remaining 40 c

1.	The face cards are removed from a full pack. Out of the remaining 40 cards, 4 are drawn at random. What is the probability that they belong to different suits?
Answer» given: pack of 52 cards from which face cards are removed Formula: P(E) = \(\frac{favorable\ outcomes}{total\ possible\ outcomes}\) four cards are drawn from the remaining 40 cards, so we have to find the probability that all of them belong to different suit total possible outcomes of drawing four cards are ⁴⁰C₄ therefore n(S)= ⁴⁰C₄ let E be the event that 4 cards belong to different suit n(E)= ¹⁰C₁ ¹⁰C₁ ¹⁰C₁ ¹⁰C₁= 10000 P(E) = \(\frac{n(E)}{n(S)}\) P(E) = \(\frac{10000}{91390}\) = \(\frac{1000}{9139}\)

The face cards are removed from a full pack. Out of the remaining 40 cards, 4 are drawn at random. What is the probability that they belong to different suits?

Answer»

given: pack of 52 cards from which face cards are removed

Formula: P(E) = \(\frac{favorable\ outcomes}{total\ possible\ outcomes}\)

four cards are drawn from the remaining 40 cards, so we have to find the probability that all of them belong to different suit

total possible outcomes of drawing four cards are ⁴⁰C₄

therefore n(S)= ⁴⁰C₄

let E be the event that 4 cards belong to different suit

n(E)= ¹⁰C₁ ¹⁰C₁ ¹⁰C₁ ¹⁰C₁= 10000

P(E) = \(\frac{n(E)}{n(S)}\)

P(E) = \(\frac{10000}{91390}\) = \(\frac{1000}{9139}\)

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