Can someone please help me

Three couples go to the movie theater. They want to seat people together for maximum enjoyment, but instead they randomly file i

Marat540 [252]

As there are 3 couples, so that means there are total 3 × 2 = 6 people altogether.

So now to make 6 people sit on 6 sits can be done in folowing ways:

suppose these are 6 seats available

_____1__ ______2___ ____3______ ___4__ ____5___ ___6____

Now there are 6 ways to make a person sit on seat 1.

Once seat 1 is occupied we are left with 5 people (1 person sat on seat 1)

so now 2nd seat can be filled in 5 ways

after 1 person sat on seat 2, then 3rd seat can be filled in 4 ways ( out of 6 people already 2 people sat on seat 1 and 2 so only 4 people left for 3rd seat)

And similarly for 4th seat can be filled in 3 ways

then 5th seat can be filled in 5 ways

then 6th seat can be filled in only 1 way.

Now as per fundamental principle of counting if there are m ways to do one event and n ways to do another event so altogether are m × n ways to do them.

So using same fundamental principle of counting here we get total ways to make 6 people sit on 6 seats as 6 × 5 × 4 × 3 × 2 × 1 or 6! = 720 ------------(1)

----------------------------------------------------------------------------------------------------

Now they want each couple to sit together. So every two particular people make one group (1 couple).

so like we saw 6 people can be seated on 6 seats in 6! ways (from (1))

similarly 3 couples can be seated in 3! or 3 × 2 × 1 = 6 ways

And 1st couple can sit in 2 ways amoung themselves (husband left wife right or wife left and husband right).

similarly 2nd couple can also sit in 2 ways amoung themselves

and 3rd couple can also sit in 2 ways amoung themselves

So altogether, by funadmental principle of counting, all 3 couples can be seated in 6 × 2 × 2 × 2 = 48 ways -----------(2)

--------------------------------------------------------------------------------------------

Probability of event is given by formula:

$Probability = \frac{Number- of- favourable-outcomes}{Total-number-of -outcomes}$

so favourable outcomes from (2) we have as 48

total number of outcomes from (1) we have 720.

so plug these value in probability formula

Probability = $\frac{48}{720}$

To reduce this fraction divide by greatest common factor in 48 and 720 which is 48. so we get

$\frac{48 \div 48}{720 \ div 48} = \frac{1}{15}$

so thats the final answer.

8 0

3 years ago

Writing and Evaluating an Algebraic Expression Try it five more than the product of two and a number, decreased by seven; evalua

Mkey [24]

Answer:

7

Step-by-step explanation:

dont trust me i dont know the answer sry

5 0

3 years ago

Please answer this question ASAP

OverLord2011 [107]

Answer:

a

im pretty sure

Step-by-step explanation:

8 0

3 years ago

If the mean of a normal distribution is 105, what is the median of the distribution? O A 315 OB. 105 O C. 420 D. 210 SUBM

Oliga [24]

Answer:

105

Step-by-step explanation:

A normal or symmetrical distribution where each the distance between each side of the distribution to the midpoint is the same, a normal distribution, also called a symmetrical distribution has the se value for both its median and mean. Hence, if the mean of a normal distribution is x, then it's median will also be x.

For the scenario given,

Since mean = 105 ; then median = 105

3 0

3 years ago

Are my answers for the conditional statement correct? I would just like to check them and if they're incorrect, could you let me

anyanavicka [17]

Statement: If p, then q

Inverse: If q, then p

Converse: If not p, then not q

Contrapositive: If not q, then not p.

We can see from the statement that p = brush teeth twice a day and q = not get cavities.

Thus:

Inverse: If I don't get cavities, then I brush my teeth twice a day. FALSE (for example, I might floss extra well instead. Brushing my teeth twice a day is not the only way to avoid cavities)

Converse: If I don't brush my teeth twice a day, then I get cavities. FALSE (for example, I might not eat a lot of sugar and thus I don't get cavities)

Contrapositive: If I get cavities, then I did not brush my teeth twice a day. TRUE

If this confuses you, try the example of p = cat and q = four legs. (i.e. the statement is If this is a cat, it has four legs). Try making the inverse, converse, and contrapositive, and see the truth of those statements.

7 0

3 years ago