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iragen [17]
3 years ago
15

Three boys and six girls are being seated in a row of nine chairs on a stage which are numbered from left to right. How many sea

ting arrangements are there if: A. There are no restrictions as to how they are seated? B. The boys sit in the middle three seats? C. Girls sit in the first two seats as well as the last seat? D. The first four seats alternate girl, boy,
Mathematics
1 answer:
OLga [1]3 years ago
3 0

Answer:

A. 362,880

B. 4,320

C. 14,400

D. 21,600

Step-by-step explanation:

A.

If there are no restrictions as to how they are seated, then we have permutations of 9 elements and there are 9! (factorial of 9) = 362,880 different seating arrangements.

B.  

If the boys sit in the middle three seats, they can sit in 3!=6 different ways, the girls can sit then in 6!=720 different ways. By the fundamental rule of counting, there are 6*720 = 4,320 different seating arrangements.

C.

We now have arrangements of the type

g, g, x, x, x, x, x, x, g  

The three girls at the ends can be chosen in C(6;3) (combinations of 6 taken 3 at a time) =  

\large \frac{6!}{3!(6-3)!}=\frac{6!}{3!3!}=20

different ways. The 6 in the middle can be sit in 6!=720 different ways.

By the fundamental rule of counting, there are 20*720 = 14,400 different seating arrangements.

D.

Now we have arrangements

g,b,g,b,x,x,x,x,x

For the 1st position we have 6 possibilities, for the 2nd we have 3 possibilities, for the 3rd we have 5 possibilities and for the 4th we have 2 possibilities. For the last 5 we have 5!=120 possibilities.

By the fundamental rule of counting, there are 6*3*5*2*120 = 21,600 different seating arrangements.

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Answer:

{5}^{7}

Step-by-step explanation:

5^3•5^4 =  {5}^{3 + 4}  =  \purple{ \bold{ {5}^{7} }}

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3 years ago
You are building a scale model of a fishing boat. The boat is 62 ft long and 23 ft wide. The
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The wide of the model should be approximately 5.194 inches

Step-by-step explanation:

You are building a scale model of a fishing boat

  • The boat is 62 ft long
  • The boat is 23 ft wide
  • The model will be 14 in long

We need to find how wide should it be

∵ The boat is 62 feet long

∵ The model of the boat is 14 inches long

- That means 14 inches represents 62 feet

By using the ratio method

→ Actual (ft)    :    Model (in)

→ 62               :    14

→ 23               :     x

By using cross multiplication

∵ 62 × x = 23 × 14

∴ 62 x = 322

- Divide both sides by 62 to find x

∴ x ≅ 5.194

∵ x represents the wide of the model

∴ The wide of the model is approximately 5.194 inches

The wide of the model should be approximately 5.194 inches

Learn more:

You can learn more about the scale drawing in brainly.com/question/570757

#LearnwithBrainly

5 0
3 years ago
For a segment of a radio show a disc jockey can play 10 records. If there are 12 records to select from in how many ways can the
sveta [45]

Answer:

<h2>66 different ways </h2>

Step-by-step explanation:

This is a combination question. Combination has to do with selection. For example if r objects are to be selected from n pool of oblects, this can be done in nCr number of ways.

nCr = n!/(n-r)r!

According to the question, if a radio show can only play 10 records out of 12 records available, this can be done in 12C10 number of ways.

12C10 = 12!/(12-10)!10!

= 12!/2!10!

= 12*11*10!/2*10!

= 12*11/2

= 6*11

= 66 different ways

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The slope represents the cost per gallon for heating oil while the y-intercept represents the fee for heating oil.

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2 years ago
What is 321 over 100 in simplest form?
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321 / 100 = 3.21 as you are dividing by 10, and then 10 again
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