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
gregori [183]
2 years ago
11

A deck of cards contains 30 cards with labels 1, 2, . . . , 30. Suppose that somebody is randomly dealt a set of 7 cards of thes

e cards (numbered with seven distinct numbers). a) Find the probability that 3 of the cards contain odd numbers and 4 contain even numbers. b) Find the probability each of the numbers on the seven cards ends with a different digit. (For example, the cards could be 3, 5, 14, 16, 22, 29, 30.
Mathematics
1 answer:
____ [38]2 years ago
4 0

\displaystyle |\Omega|=\binom{30}{7}=\dfrac{30!}{7!23!}=\dfrac{24\cdot25\cdot\ldots\cdot30}{2\cdot3\cdot\ldots\cdot 7}=2035800

a)

\displaystyle\\|A|=\binom{15}{3}\cdot \binom{15}{4}=\dfrac{15!}{3!12!}\cdot\dfrac{15!}{4!11!}=\dfrac{13\cdot14\cdot15}{2\cdot3}\cdot\dfrac{12\cdot13\cdot14\cdot15}{2\cdot3\cdot4}=13\cdot7\cdot5\cdot13\cdot7\cdot15=621075\\\\P(A)=\dfrac{621075}{2035800}=\dfrac{637}{2088}\approx30.5\%

b)

\displaystyle\\|A|=\binom{10}{7}\cdot 3^7=\dfrac{10!}{7!3!}\cdot2187=\dfrac{8\cdot9\cdot10}{2\cdot3}\cdot2187=4\cdot3\cdot10\cdot2187=262440\\\\P(A)=\dfrac{262440}{2035800}=\dfrac{243}{1885}\approx12.9\%

You might be interested in
Factor X-7X -5x + 35 by grouping. What is the resulting expression?
Yuliya22 [10]
The answer is c). (x-5)(x-7)
7 0
4 years ago
How many gallons of water could a 5 feet by 2 feet by 2 feet aquarium hold? How much the 150 gallons of water would weigh?
Marianna [84]

Answer:

V = (5 feet) (2 feet) (2 feet) V = 20 cubic feet To convert the volume into gallons, multiply the above answer by 7.48 since there are 7.48 gallons of water in one cubic foot. This will give us an answer of 150 gallons of water.

Step-by-step explanation:

4 0
2 years ago
Determine the radius of a circle with a circumference of 14 pi inches ​
ipn [44]

Answer:

the radius is 7

Step-by-step explanation:

circumference is equal to pi(d)

you said it is 14pi

all you have to do is divide d by 2 to get r

7 0
3 years ago
In a bird sanctuary, 30% of the birds are
Sauron [17]

Answer:  105 of them are hummingbirds.

Step-by-step explanation:

I there are a total of 350  birds then 30% o 350 will give the number o hummingbirds.

350 of 30%

350 * 0.3 = 105

7 0
3 years ago
Es
daser333 [38]

Answer:

not clear

Step-by-step explanation:

can you please retype the question? the greatest mathematician is here to help you.

8 0
4 years ago
Read 2 more answers
Other questions:
  • The tax rate on Jerome James 112000 vacation home is 25 Mills the property is assessed at full value how much will Jerome pay in
    6·2 answers
  • Amy bought 0.4 kg of tomatoes for $4.00.<br><br> What is the cost in dollars per kg of tomatoes?
    8·2 answers
  • Please Help!!!
    14·1 answer
  • Need an answer as soon as possible thank you :}
    5·1 answer
  • A "centroid" is defined as the center of mass of an object, or shape. How might the midpoint formula be used to find the midpoin
    6·1 answer
  • 1+1<br> NEED HELP LOL<br> urgent<br> help
    11·2 answers
  • I need help I’ll give u brainlest
    12·1 answer
  • 2/3 divided 1/4 , give answers in simplest form
    15·1 answer
  • What is 2 + 2 + 3 x 4 - 1 x 10 - 6. First on the answer gets brainlist;)
    15·1 answer
  • I need help with this one some one help pls
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!