permutation problem

[TimeforDAT]

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6 sets of numbers are given: 6, 0, 0, 1, 0, 1

how many different ways can they be arranged?



I'm not sure how they got it. the solution says there are 3 "zeros" and 2 "ones" alike. the permutations of the six numbers are


6!/(3!2!) = 60

can someone explain why they did that? i thought they were suppose to use the nCr formula

thanks

 

[HeatingHomer]

nCr is only used when each of the numbers is different.

 

[Streetwolf]

Do a search!

 

[allday0109]

6 sets of numbers are given: 6, 0, 0, 1, 0, 1

how many different ways can they be arranged?



I'm not sure how they got it. the solution says there are 3 "zeros" and 2 "ones" alike. the permutations of the six numbers are


6!/(3!2!) = 60

can someone explain why they did that? i thought they were suppose to use the nCr formula

thanks

I am not sure this is correct
just guess there are 6 boxes in row
then, when you put one number into the box there are six possibilities to put and then 5, and so on. but there are three zeros and two ones, so you need to divide it by the possibilities that same arrangements are made by using those same number.
I hope this helps

 

[navajoDDS]

Google: permutations with like objects

you have to take into account any number that repeats itself, or you will be counting the same arrangement multiple times.

ex. how many arrangements of 2 are there from 6,0,0
60, 60, 06, 06, 00, 00. there are only 3 different possibilities.

Use this equation: n!/[(r1!)(r2!)...(rk!)] where r=# of repeats

This might not help much, but I'm sure you can find some good info if you google it!

 

[TimeforDAT]

Google: permutations with like objects

you have to take into account any number that repeats itself, or you will be counting the same arrangement multiple times.

ex. how many arrangements of 2 are there from 6,0,0
60, 60, 06, 06, 00, 00. there are only 3 different possibilities.

Use this equation: n!/[(r1!)(r2!)...(rk!)] where r=# of repeats

This might not help much, but I'm sure you can find some good info if you google it!

thanks!