Question

.8 women and 6 men are standing in a line.
(i) How many arrangements are possible if any individual can stand in any position?
(ii) In how many arrangements will all 6 men be standing next to one another?
(iii) In how many arrangements will no two men be standing next to one another?
please answer this question​

Answer 1

Step-by-step explanation:

Given :-

Current drawn by filament of an electric bulb = 25 A

Time taken by the electric bulb = 10 m

To Find :-

The amount of electric charge that flows through the circuit.

Analysis :-

Here we are given with the current and time taken by the electric bulb.

In order to find the charge flown substitute the values given in the question such that charge flown is equal to current multiplied by the time.

Solution :-

We know that,

i = Current

q = Charge

t = Time

Using the formula,

\underline{\boxed{\sf Charge=Current \times Time}}

Charge=Current×Time

Given that,

Current (i) = 25 A

Time (t) = 10 min = 600 sec

Substituting their values,

⇒ q = i × t

⇒ q = 25 × 600

⇒ q = 15000 C

⇒ q = 1.5 × 10⁴

Therefore, the amount of electric charge that flows through the circuit is 1.5 × 10⁴.

Answer 2

When you deal with ARRANGEMENTS, you use permutations.

Imagine a real life scenario, no man and no women can be the same, no 2 men or women can be the same.

Everyone in that queue is a different person and hence is unique.

You cannot use Combinations in this case as it is arrangements not selection.

So since the men are more, keep them in a line with gaps between them. So 8 men, means, 7 gaps + 2 gaps on the ends.

So the women have 9 spaces to occupy, but only 5 women, so 9P5.

The men can also exchange places with each other, so 8P8.

You multiply them because for each man changing position, there are 9P5 ways for the women.

I hope this helps