Using a 52 card deck, how many 5 card hands have either 5 hearts or 4 hearts and 1 club

Answers

answer:   \frac{sin40^{\circ}}{x} = \frac{sin60^{\circ}}{12}

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

\frac{sin40^{\circ}}{x} = \frac{sin60^{\circ}}{12}

which is the required equation for finding the value of x,

\frac{x}{sin40^{\circ}}= \frac{12}{sin60^{\circ}}

x= 12\times \frac{sin40^{\circ}}{sin60^{\circ}}

x= 12\times 0.74222719896

x= 8.90672638762\approx 8.967

use google you idiot omg you're so annoying

step-by-step explanation:

10,582

Step-by-step explanation:

We can choose 5 cards from 52 card deck in

      n = \binom{52}{5} = \frac{52!}{5!(52-5)!}  = \frac{52!}{5!47!} = \frac{\cancel{47!} \cdot 48 \cdot 49 \cdot 50 \cdot 51 }{5! \cancel{47!}} = \frac{ 48 \cdot 49 \cdot 50 \cdot 51 }{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5}  = 2 \; 598 \; 960

ways.

Now, let's calculate the number of ways we can choose 5 hearts. We know that in a 52 card deck, we have 13 hearts. Therefore, the number of ways to choose 5 hearts is

       n_1 = \binom{13}{5} = \frac{13!}{5!(13-5)!} =  \frac{13!}{5!8!} = \frac{8! \cdot 9 \cdot 10 \cdot 11 \cdot 12 \cdot 13}{5!8!} = \frac{9 \cdot 10 \cdot 11 \cdot 12 \cdot 13}{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5} = 1287

Similarly, number of ways to choose 4 hearts equals \binom{13}{4} and number of ways to choose 1 club equals \binom{13}{1}, since there are also 13 clubs in the deck.

Therefore, the number of ways of choosing 4 hearts and 1 club equals

                                   n_2 = \binom{13}{4} \cdot \binom{13}{1} = 9295

The probability of this event is calculated as

           P(A) = \frac{\text{total number of ways to choose 5 hearts or 4 hearts and a club}}{\text{total number of ways to choose 5 cards from a deck of 52 cards}}

Therefore

                     P(A) = \frac{n_1+n_2}{n} = \frac{1287+9295}{2598960} =0.0040716 \approx 0.0041



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