HELP---QR problem

[navneetdh]

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How many Different ways can a data consisting of 6, 0, 0, 1, 0, 1 be arranged??

I thought this was permutations right??

ok so i did

n=6
r=3 (3 different types of numbers)

so its like 6!/(6-3)! = 6!/3!

But nooooooo

achiever says it is

6!/3!2!

I have no clue what the hell is that???

ca someone plz explain?🙁

 

[arginine1]

6! is your total number of elements, but you have to account for the fact that there is three zeros and two ones ( so there are 3 same elements, as is three zeros and another pair of same elements as in two ones)

that's why you divide by the number of indistinguishable elements in you data set (that would be 3! for three zeros and 2! for two ones)

I'm sorry I can't make it sound clearer.. just think about the fact that there are repeating elements so changing their position would not change the overall arrangement and you have to account for that in some way.

 

[yumi43]

the 3! accounts for the three 0's, and the 2! accounts for the two 1's.

since you are given multiple 0's and 1's in this set, there isn't any way to distinguish between one 0 from another 0, or one 1 from another 1, etc. so if you didn't take this into account, you'd just have duplicate permutations.

so when you have a set where some elements are indistinguishable, calculate the factorial of the total number of elements and divide by the factorial(s) of the number of indistinguishable elements.

 

[navneetdh]

cool guys!! thanks a lot. I wasnt aware of this formula/property