Combinatorics...

jjenrico wrote:hi guys,

can you help me with this?

How many different signals can be transmitted by hoisting 3 red, 4 yellow and 2 blue flags on a pole, assuming that in transmitting a signal all nine flags are to be used?

I don't have the options, but how do I approach it??

thanks!

9!/(3! *4! * 2!)

x2suresh

can you pls explain why?

thanks!

total combinations possible (9!) / possibilities you have (4! of the yellow flags * 3! combinations of Red * 2! combinations of the blue)

Answer should be 15120

The question is asking in how many ways can you arrange the letters RRRYYYYBB

The number of ways of arranging 9 flags = 9!

Now we divide 3!*4!*2! to account for the letters that are repeated.

So the answer should be 9!/3!*4!*2!

There are two different permutations formulas that it's good to know for Test Day.

1) If we have n unique items and we want to arrange k of them, then the total number of arrangements is:

n!/(n-k)!

2) If we have n items to arrange, but some of them are identical, then the total number of arrangements is:

n!/r!s!t!...

in which r, s and t are the number of duplicate items.

This is most commonly tested on the GMAT in word jumble questions. Here are some examples:

In how many different ways can the letters of the word "DESERT" be arranged?

6 total letters, 2 duplicate "E"s, so 6!/2!

In how many different ways can the letters of the word "DESSERT" be arranged?

7 total letters, 2 duplicate "E"s and 2 duplicate "S"s so 7!/2!2!

In how many different ways can the letters of the word "DESSERTS" be arranged?

8 total letters, 2 duplicate "E"s and 3 duplicate "S"s, so 8!/2!3!

In the question posted in this thread, we have 9 total items with 3 duplicate reds, 4 duplicate yellows and 2 duplicate blues, so our answer is:

9!/3!4!2!