Question

1)n!/a!xb!xc! 2) n! / (n-r)! 3)n!/(n-r)! x r!

I was given this three formulas but i dont know how to apply them ! May i know how can i apply them ?

Answer 1

the second one is for permutation and the third one is for combination

Answer 2

first one is for arrangemnts of n objects of which a are of one type, b are of another type and c of another

Answer 3

nCr = (nPr)/r :)

Answer 4

you told that one :P

Answer 5

good morning joemath!

Answer 6

an example of a problem that would use the first formula is:
you have 4 red blocks, 5 green blocks, and 7 blue blocks. How many ways can you rearrange the order of the blocks and be able to tell the difference?
good morning satellite!

Answer 7

No i meant 16 ! / 4! x 5! x 7!

Answer 8

you need the total number of blocks on the top. so it would be:
\[\frac{16!}{4!5!7!}\]
ah yes, thats what it would be, nice :)

Answer 9

Do you mind giving me an example for the second and third formula?

Answer 10

Sure, for the second equation:
If you have 20 people in a race, and 1st place, second place, and third get medals, how many different ways can the medals be handed out to the 20 people? ( i might be making this one sound more complicated than it is >.<)

Answer 11

For the third equation:
i have a box full of 10 stuffed animals, and im going to pick 3 to put on my desk. How many different ways can I pick 3 stuffed animals from the group of 10?

Answer 12

20!/ (20-3)! ? Haha thanks a lot . Is it ? I 'm not too sure .

Answer 13

yes thats correct :)

Answer 14

10!/(10-3)! X 3! ?

Answer 15

yes that is also correct :)

Answer 16

Thanks a lot. But like how can i know which formula to use for which qn ?

Answer 17

you really have to memorize what scenario is going on. For the first formula, you are mixing up items, but some of the items look identical to the others. Take the blocks for example. If i have an order like, "rrrbbbgg" or whatever, if i switch 2 red without you looking, you wouldnt be able to tell. A situation like that calls for the first formula.

Answer 18

The second is use for things like the race, where we have "positions" that people or objects can obtain, and order matters. The race for example. Billy, Sally, and Sue getting 1st, 2nd, and 3rd is different than Sally, Billy, and Sue. Order matters, and the second formula takes care of that.

Answer 19

In the third, order doesnt matter. If i pulled out a bunny, cat, and bear out of the box to put on my desk, that would be the same result if i pulled out a bear, bunny, and a cat. Order doesnt matter in this scenario, and the third equation models that.

Answer 20

Thanks so much for clearing the doubts I had for today !!!!

Answer 21

no prob :)