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3 years ago

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A group of eight friends (five girls and three boys) plans to watch a movie but they have only five tickets how many different c

ombinations of five friends could possibly receive the tickets

1 answer:

nirvana33 [79]3 years ago

6 0

1- all five girls

2- four girls and one boy

3. three girls and two boys

4. two girls and three boys.

4 combinations

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2. In how many ways can 3 different novels, 2 different mathematics books and 5 different chemistry books be arranged on a books

insens350 [35]

The number of ways of the books can be arranged are illustrations of permutations.

When the books are arranged in any order, the number of arrangements is 3628800
When the mathematics book must not be together, the number of arrangements is 2903040
When the novels must be together, and the chemistry books must be together, the number of arrangements is 17280
When the mathematics books must be together, and the novels must not be together, the number of arrangements is 302400

The given parameters are:

$\mathbf{Novels = 3}$

$\mathbf{Mathematics = 2}$

$\mathbf{Chemistry = 5}$

<u />

<u>(a) The books in any order</u>

First, we calculate the total number of books

$\mathbf{n = Novels + Mathematics + Chemistry}$

$\mathbf{n = 3 + 2 + 5}$

$\mathbf{n = 10}$

The number of arrangement is n!:

So, we have:

$\mathbf{n! = 10!}$

$\mathbf{n! = 3628800}$

<u>(b) The mathematics book, not together</u>

There are 2 mathematics books.

If the mathematics books, must be together

The number of arrangements is:

$\mathbf{Maths\ together = 2 \times 9!}$

Using the complement rule, we have:

$\mathbf{Maths\ not\ together = Total - Maths\ together}$

This gives

$\mathbf{Maths\ not\ together = 3628800 - 2 \times 9!}$

$\mathbf{Maths\ not\ together = 2903040}$

<u>(c) The novels must be together and the chemistry books, together</u>

We have:

$\mathbf{Novels = 3}$

$\mathbf{Chemistry = 5}$

First, arrange the novels in:

$\mathbf{Novels = 3!\ ways}$

Next, arrange the chemistry books in:

$\mathbf{Chemistry = 5!\ ways}$

Now, the 5 chemistry books will be taken as 1; the novels will also be taken as 1.

Literally, the number of books now is:

$\mathbf{n =Mathematics + 1 + 1}$

$\mathbf{n =2 + 1 + 1}$

$\mathbf{n =4}$

So, the number of arrangements is:

$\mathbf{Arrangements = n! \times 3! \times 5!}$

$\mathbf{Arrangements = 4! \times 3! \times 5!}$

$\mathbf{Arrangements = 17280}$

<u>(d) The mathematics must be together and the chemistry books, not together</u>

We have:

$\mathbf{Mathematics = 2}$

$\mathbf{Novels = 3}$

$\mathbf{Chemistry = 5}$

First, arrange the mathematics in:

$\mathbf{Mathematics = 2!}$

Literally, the number of chemistry and mathematics now is:

$\mathbf{n =Chemistry + 1}$

$\mathbf{n =5 + 1}$

$\mathbf{n =6}$

So, the number of arrangements of these books is:

$\mathbf{Arrangements = n! \times 2!}$

$\mathbf{Arrangements = 6! \times 2!}$

Now, there are 7 spaces between the chemistry and mathematics books.

For the 3 novels not to be together, the number of arrangement is:

$\mathbf{Arrangements = ^7P_3}$

So, the total arrangement is:

$\mathbf{Total = 6! \times 2!\times ^7P_3}$

$\mathbf{Total = 6! \times 2!\times 210}$

$\mathbf{Total = 302400}$

Read more about permutations at:

brainly.com/question/1216161

8 0

2 years ago

What is 7.214 rounded to the nearest hundredths

Olin [163]

7.214 rounded to the nearest hundredth is 7.21<span />

7 0

4 years ago

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Please answer the question in the image

seraphim [82]

Answer:

- $\frac{1}{14}$

Step-by-step explanation:

Given

$\frac{1}{2}$ × - $\frac{1}{7}$ ( multiply numerators and denominators together )

= - $\frac{1(1)}{2(7)}$

= - $\frac{1}{14}$

7 0

3 years ago

two cars start from two towns 400 miles apart and travel towards each other. They pass each other after 4 hours. find the speed

Gemiola [76]

<span>use an expression
s = speed of the slower car
then
(s+20) = speed of the faster car

When they meet is after 400 miles

Write distance equation

slow car d + fast car d = 400 mi
4s + 4(s+20) = 400

8s + 80 = 400

8s = 400 - 80

8s = 320

s = 40 m/H</span>

5 0

3 years ago

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1/3 x =6 What would like match this answer

Bumek [7]

Answer:

x=18

Step-by-step explanation:

6 0

3 years ago

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