Help with Permutations and Combinations (1 Viewer)

[bored of sc]

What techniques are needed in order to effectively solve permutation and combination questions every time???

Diagrams with scribbling on them, taking each step one at a time, checking your working thoroughly, getting realistic solutions and linking parts (a) (b) etc in questions.

But what else.

Here's a hard example (hard for me):

At a dinner party 6 people sit around a table.
Find the probability that if seating is at random, 2 friends will sit apart.

Thank you!

 

[foram]

What techniques are needed in order to effectively solve permutation and combination questions every time???

Diagrams with scribbling on them, taking each step one at a time, checking your working thoroughly, getting realistic solutions and linking parts (a) (b) etc in questions.

But what else.

Here's a hard example (hard for me):

At a dinner party 6 people sit around a table.
Find the probability that if seating is at random, 2 friends will sit apart.

Thank you!

Ways people can sit around a table: 5!
(circular arrangement means they are arranged in relation to one person, so that one person is excluded when counting the number of ways.)

Ways 2 friends can sit together 4! x 2!
(treat the 2 friends as one object which can be arranged in 2! ways)

Ways 2 friends can NOT sit together: 5! - (4! x 2!) = 72
(Total number of ways, subtract the number of ways which they will sit together. Then you're left with the number of ways that they can sit apart.)

Thats how i think it's done. Permutations and combinations at a 3U standard is very easy. Don't stress. I have never scribled diagrams before, unless they were incomplete tree diagrams for 2U math. I find diagrams for Permutations and Combinations to be absolutely useless, but people learn differently. If you feel like using them, then by all means do so.

 

[foram]

Also, remember that if they give you a questions about beads on a necklace, divide your answer by 2 because the beads can be reversed in order by flipping it around.

 

[bored of sc]

thanks heaps for that foram - you got it spot on

thanks also for that very handy beads tip

 

[Aerath]

Thanks Foram.