### Basics Concepts and Formulas in Permutations and Combinations

sreekanth

2015-12-18 07:08:58

I have a doubt the number of ways to wear 6 ring in 4 fingers is 4^6 but why not 6^4

Anish

2016-01-23 15:01:57

In the above problem, you cannot think it like-

1st finger can be put in 6 rings

2nd finger can be put in 6 rings

...

4th finger can be put in 6 rings.

therefore total no. of ways=6^4

Because if you do so , you will consider two or more fingers can be put into a single ring, which is not possible.

so you cannot think the problem like that.

1st finger can be put in 6 rings

2nd finger can be put in 6 rings

...

4th finger can be put in 6 rings.

therefore total no. of ways=6^4

Because if you do so , you will consider two or more fingers can be put into a single ring, which is not possible.

so you cannot think the problem like that.

sam

2015-12-22 12:56:50

We have to think it in this way.

1st ring can go into any of the 4 fingers

2nd ring can go into any of the 4 fingers

3rd ring can go into any of the 4 fingers

4th ring can go into any of the 4 fingers

5th ring can go into any of the 4 fingers

6th ring can go into any of the 4 fingers

therefore answer is 4*4*4*4*4*4 = 4^6

1st ring can go into any of the 4 fingers

2nd ring can go into any of the 4 fingers

3rd ring can go into any of the 4 fingers

4th ring can go into any of the 4 fingers

5th ring can go into any of the 4 fingers

6th ring can go into any of the 4 fingers

therefore answer is 4*4*4*4*4*4 = 4^6

Hemant

2015-10-25 09:58:31

How do I generate Permutation dynamically where number of position are dynamic and per position possible option is again dynamic?

e.g. I want to pick up 4 number (here 4 number is dynamic) n1n2n3n4

and again for each number position i.e. 1 to 6 possible option will be dynamic.

1 st number could be = 1,2,3

2nd number could be = 1

3rd number could be = 1,2

4th number could be = 5,6,7

any algorithm get all those permutation?

e.g. I want to pick up 4 number (here 4 number is dynamic) n1n2n3n4

and again for each number position i.e. 1 to 6 possible option will be dynamic.

1 st number could be = 1,2,3

2nd number could be = 1

3rd number could be = 1,2

4th number could be = 5,6,7

any algorithm get all those permutation?

Shiksha

2015-01-12 18:17:16

Hi,

I have a question, if we have 6 white balls, 3 blue balls and 2 Red balls and we have to pick a selection 4?

a) how many combinations it will be?

b) if always 2 white have to be selected from 4 then how many combinations possible?

I have a question, if we have 6 white balls, 3 blue balls and 2 Red balls and we have to pick a selection 4?

a) how many combinations it will be?

b) if always 2 white have to be selected from 4 then how many combinations possible?

Shraya

2015-08-17 17:09:13

a). Your head question and part a both depict the same. Picking any four irrespective of the color.

So, 6 + 3 + 2 = 11.

11C4 = @@\dfrac{11!}{4!×(11-4)!}=11×10×3=330@@

b) The 2nd part i think you didn't give a clarity. Out of 4 if at least two must be white.

then,

picking 4 whites out of 6 whites = 6C4

picking 3 whites with 1 blue or red = 6C3 × 3C1 × 2C1

picking 2 whites with 2 blue = 6C2 × 3C2

picking 2 whites with 2 red = 6C2 × 2C2

picking 2 whites with 1 red 1 blue = 6C2 × 3C1 × 2C1

Now multiply all.

So, 6 + 3 + 2 = 11.

11C4 = @@\dfrac{11!}{4!×(11-4)!}=11×10×3=330@@

b) The 2nd part i think you didn't give a clarity. Out of 4 if at least two must be white.

then,

picking 4 whites out of 6 whites = 6C4

picking 3 whites with 1 blue or red = 6C3 × 3C1 × 2C1

picking 2 whites with 2 blue = 6C2 × 3C2

picking 2 whites with 2 red = 6C2 × 2C2

picking 2 whites with 1 red 1 blue = 6C2 × 3C1 × 2C1

Now multiply all.

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2015-08-17 16:47:51

This question has been moved to Discussion Board. Click here to view.

Pankaj Sharma

2015-08-07 11:52:03

as coming to your que 1

1) we can select any 4 balls out of (6B,3B,2R) so total combinations are 11C4

2)now in the second part exactly 2 balls are white so combinations are 6C2*5C2

1) we can select any 4 balls out of (6B,3B,2R) so total combinations are 11C4

2)now in the second part exactly 2 balls are white so combinations are 6C2*5C2

Guglani

2015-08-17 15:53:00

i got the point i.e 6C2, here you select 2 balls from all six white balls,

but u can have all the white balls also, i.e 4.

i think there would be 6C2*9C2 ??

isn't it !!!

but u can have all the white balls also, i.e 4.

i think there would be 6C2*9C2 ??

isn't it !!!

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