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
djverab [1.8K]
3 years ago
12

In how many ways can you place 50 identical balls in six distinct urns such that each urn contains an odd number of balls

Mathematics
1 answer:
mezya [45]3 years ago
8 0

Answer:

80730

Step-by-step explanation:

The answer is c(27,5)=27*26*25*24*23/5!. Here is why.

Let us solve a simpler problem. In how many ways 25 identical balls can be placed in six distinct urns such that no urn is empty?

25 balls in a row make 24 places for five dividers, so the answer is c(24,5).

2. Next problem. In how many ways 50 identical balls can be placed in six distinct urns such that no urn is empty and each urn contains even number of balls.

We group 50 balls in 25 pairs, so the answer is the same as in the previous problem which is

c(48/2,5)=c(24,5).

Let us denote the content of each urn as

u(1),u(2),…u(6). Note that each u(i) is even. Denote u(i) as u(i)=2k(i) where k is a natural number. We have

2k(1)+2k(2)+2k(3)+2k(4)+2k(5)+2k(6)=50.

3. Now let us proceed to the original problem where odd number of balls in each urn is required.

We have

2k(1)-1+2k(2)-1+2k(3)-1+2k(4)-1+2k(5)-1+2k(6)-1=50 or

2k(1)+2k(2)+2k(3)+2k(4)+2k(5)+2k(6)=56.

So the original problem reduces to previous problem where even number of balls in each urn is required but the total number of balls is 56 instead of 50.

Its answer is c(54/2,5)=c(27,5).

You might be interested in
Please help me to solve these questions as soon as possible. Thank you ​
densk [106]

Answer:

499

9

April 12 2021

Step-by-step explanation:

1 and 500 are the smallest and largest

12 is the highest common factor

Every 12 days they have an appointment together

8 0
3 years ago
The pair of figures are simular.find the value of each variable
kkurt [141]
Y=12 because the triangles have proportional side lengths
5 0
3 years ago
Level 3<br> 6 2<br> 1 3 <br> 5 4<br> 3 2<br> Enter the correct 4 digit code (no spaces) *
aev [14]

Answer:don’t understand

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Read the excerpt from “Raymond's Run.” But now, if anybody has anything to say to Raymond, anything to say about his big head, t
dsp73

Answer:

D.  She uses Squeaky’s thoughts and words to tell readers about her character.

3 0
3 years ago
Read 2 more answers
A triangle with which angle types could be constructed?
kifflom [539]

Answer:

B is the answer.

Step-by-step explanation:

*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^

Triangles cannot have two 90 degrees because that would add up to 180 and triangles need 3 angles to add to 180

You can't have an obtuse angle and a right angle. say the obtuse angle was 110, and a right angle is 90. 110 + 90 is more than 180.

Two obtuse angles would be more than 180.

This leaves us with B being correct, because you can have an obtuse angle and an acute angle, and it can be less than 180 degrees.

*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^

#teamtrees #WAP (Water And Plant)

5 0
3 years ago
Read 2 more answers
Other questions:
  • Can someone please answer these questions?
    14·1 answer
  • Taking Test need Help!
    9·2 answers
  • Solve Using The Square Root Property . - Show Work<br><br> 3x^2 + 27 = - 108
    10·1 answer
  • A diver begins at 150 feet below sea level, descends at a steady rate of 5 feet per minute for 3.5 minutes, and then ascends 122
    11·2 answers
  • What’s the correct answer for this?
    7·1 answer
  • Classify the triangle based on side lengths 2, 10 and 11
    12·1 answer
  • The temperature was 48°F and dropped 15° in two hours.
    12·2 answers
  • Is this a linear relation 2x+2y=8​
    7·1 answer
  • Please answer and make sure you’re 100% right
    10·1 answer
  • THE PROBABILITY OF AN EVENT IS 0.34. WHAT IS THE PROBABILITY THAT IT WILL NOT OCCUR.​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!