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Lina20 [59]
3 years ago
8

Suppose that 3 cards are drawn from a well-shuffled deck of 52 cards. What is the probability that all 3 are diamonds?

Mathematics
1 answer:
Marat540 [252]3 years ago
5 0

There are 13 diamonds in the deck, so \dbinom{13}3 ways of drawing 3 diamonds.

There is a total of \dbinom{52}3 ways of drawing any 3 cards from the deck.

So the probability of drawing 3 diamonds is

\dfrac{\binom{13}3}{\binom{52}3}=\dfrac{11}{850}\approx0.012941

where \dbinom nk=\dfrac{n!}{k!(n-k)!}.

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Option a: 4x^{3} -\frac{2}{x}

Option b: 2y^{3} +5y^{2} -5y

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The highest degree of a polynomial is the largest exponent of that variable.

Now, we shall determine the polynomial with degree 3.

Option a: 4x^{3} -\frac{2}{x}

From the expression 4x^{3} -\frac{2}{x}, the highest degree of the polynomial is 3.

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Hence, Option a is the correct answer.

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Hence, 2y^{3} +5y^{2} -5y is a polynomial with a degree of 3.

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