Combination/Perm Q (1 Viewer)

[Jackee]

Eight children consisting of 3 boys and 5 girls are to be seated in a row. In how many ways can this be achieved if no boys are allowed to be seated next to each other?

answer is 14400, is there an easy way way to do this question?> it was in question 2 and 2 marks.

 

[pLuvia]

That just means the boys and girls have to alternate

5!x6P3=14400

There are 6 spaces for the boys to go into between the girls and one on either side of the ends so you arrange the boys in 6P3 ways also considering the girls can be arranged in 5! ways

 

[lyounamu]

That just means the boys and girls have to alternate

5!x6P3=14400

There are 6 spaces for the boys to go into between the girls and one on either side of the ends so you arrange the boys in 6P3 ways also considering the girls can be arranged in 5! ways

can you explain this part again please? How did you deduce 6P3?

 

[undalay]

Insertion method.

You can arrange the girls in 5! ways.
Now you "insert" the boys between the girls. There's 6 slots u can insert between the girls. Since you have 3 boys, you choose 3 from 6 slots. 6C3.
Since u can rearrange the boys u multiply by 3!

= 5!6C3 x 3!
= 5!6P3

It's easier to explain with a diagram but i cbf right now to draw 1.

 

[lyounamu]

Insertion method.

You can arrange the girls in 5! ways.
Now you "insert" the boys between the girls. There's 6 slots u can insert between the girls. Since you have 3 boys, you choose 3 from 6 slots. 6C3.
Since u can rearrange the boys u multiply by 3!

= 5!6C3 x 3!
= 5!6P3

It's easier to explain with a diagram but i cbf right now to draw 1.

Ok, that's how he derived it. Thanks for clarifying that part up.

 

[whoisurdaddy]

Can someone explain the insertion method in a little more detail?
Why are there 6 slots to insert between the girls?

 

[undalay]

technically there are 4 slots between the girls.
but two more on the end(one on left one on right)

so there's 6.

If you use ur hand (with fingers being girls)
Theres 4 spaces between fingers, and two slots on the sides of ur hand.

If there were some condition that said
"the boys cannot occupy the ends of the line"
then there would jsut be 4 spaces, rather than 6.

 

[lyounamu]

Then what about this question:

The letters of the word - REPETITION - are arranged at random in a row

i) what is the chance that one particular arrangement will have vowels and consonants alternating?

Is it just:

2 x 5!/(2!2!) x 5!/(2!2!)?

 

[undalay]

Then what about this question:

The letters of the word - REPETITION - are arranged at random in a row

i) what is the chance that one particular arrangement will have vowels and consonants alternating?

Is it just:

2 x 5!/(2!2!) x 5!/(2!2!)?

almost
2 x 5!/(2!2!) x 5!/2!

since there's only 1 pair of repeating consonants

 

[lyounamu]

almost
2 x 5!/(2!2!) x 5!/2!

since there's only 1 pair of repeating consonants

There are two Ts though.

EDIT: Yeah, that was so stupid. I wrote it wrongly.