1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Aleonysh [2.5K]
3 years ago
6

A deck of 52 cards contains 12 picture cards. If the 52 cards are distributed in a random manner among four players in such a wa

y that each player receives 13 cards, what is the probability that each player will receive three picture cards
Mathematics
1 answer:
Mkey [24]3 years ago
6 0

Answer:

The probability that each player will receive three picture cards = 0.0324

Step-by-step explanation:

As given,

A deck of 52 cards contains 12 picture cards

Remaining card = 52 - 12 = 40

So,

Total number of ways in which 12 picture card is distributed = \frac{12!}{3! 3! 3! 3!}

Now,

The Total number of ways in which Remaining cards are distributed = \frac{40!}{10! 10! 10! 10!}

So,

Total number of ways of getting 3 picture card and remaining card = \frac{12!}{3! 3! 3! 3!}× \frac{40!}{10! 10! 10! 10!}

= \frac{12! 40!}{(3!)^{4} (10!)^{4}  }

Now,

Total number of ways to distribute 52 cards so that each people get 13 card = \frac{52!}{13! 13! 13! 13!} = \frac{52!}{ (13!)^{4} }

∴ The probability = \frac{\frac{12! 40!}{(3!)^{4} (10!)^{4}  }}{\frac{52!}{(13!)^{4} }}

                            = \frac{12! 40!}{(3!)^{4} (10!)^{4}  }×\frac{(13!)^{4} }{ 52! }

                           = \frac{12! 40!}{(3!)^{4} (10!)^{4}  }×\frac{(13.12.11.10!)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41.40! }

                           = \frac{12!}{(3!)^{4}   }×\frac{(13.12.11)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41}

                           = \frac{479,001,600}{(6)^{4}   }×\frac{(1716)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41}

                           = 0.0324

∴ we get

The probability that each player will receive three picture cards = 0.0324

You might be interested in
W is the midpoint of . If UW = x + 23, and WV = 2x + 8, what is WU?
kicyunya [14]
<span>-(x + 23) as WU is the same as UW but negative</span>
6 0
3 years ago
Sharon inherited ½ of her grandfather’s estate. Out of sympathy she gave away ½ of the property that she inherited. How much pro
erastova [34]

Answer:

she has a 1/4 of the property remaining

Step-by-step explanation:

8 0
3 years ago
16 - x = -18<br> A. x = -18<br> B. x = -14<br> C. x = 14 <br> D. x = 18
Leona [35]

Answer:

None of these are correct? The correct answer is 34.

Step-by-step explanation:

Subtract 16 from each side, you get -x=-34

multiply each side by -1, you get x= 34

4 0
3 years ago
Read 2 more answers
A light bulb consumes 960 watt-hours per day. How many watt-hours does it consume in 3 days and 18 hours?
oksano4ka [1.4K]

960 x 3 = 2880

18/24 = 0.75

960x 0.75 = 720

2880 + 720 = 3600

7 0
3 years ago
Read 2 more answers
4х + Зу = 9<br> find the slope and y intercept
Volgvan

Step-by-step explanation:

3y/3=9-4x/3

y=3-4x/3

slope=x= -4/3

y intercept

y=3-4(0)/3

y=3-0

y=3

7 0
2 years ago
Other questions:
  • How would you do 0.793= n+0.65
    15·2 answers
  • Find each pair of similar solids, find the ratio of the volume of the first figure to the volume of the second
    9·1 answer
  • Is 2 1/6 a irrational?
    5·1 answer
  • Given the function y = -2ex , find y if x = 3.
    11·1 answer
  • Taminka received a raise in her hourly pay, from $13.50 to $14.99. Find the percent change. Round to the nearest percent.
    10·1 answer
  • A square box has a side of 17, what is the volume, area, and perimeter of the box?
    11·2 answers
  • Find 10x+y when x= 10 and y = 3.<br> The answer is
    9·1 answer
  • 2
    10·1 answer
  • How do i estimate 13.5/5=?
    7·2 answers
  • Factor the expression using the GCF.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!