mathmath333 one year ago Counting question

1. mathmath333

\large \color{black}{\begin{align} & \normalsize \text{There are 7 people and 4 chairs. }\hspace{.33em}\\~\\ & \normalsize \text{In how many ways can the chairs be occupied.}\hspace{.33em}\\~\\ \end{align}}

2. amilapsn

We can do that in two steps. 1st step: Choosing 4 people out of 7(Combination ) 2nd step: Seating them.(Permutation)

3. mathmath333

is it 4!

4. amilapsn

In my method the answer will be this.(Giving the same as nnesha's result): $$\huge ^7C_4\times 4!$$

5. mathmath333

1st step: Choosing 4 people out of 7(Combination ) 2nd step: Seating them.(Permutation) How to implement this

6. amilapsn

$\huge \ldots=P_{(7,4)}$

7. ganeshie8

i like amilapsn's method, but here is an alternative that Nnesha is talking about : you look at 4 chairs, the first chair can have any one of the 7 persons : 7 ways after that, the second chair can have any one of the remaining 6 persons : 6 ways after that, the third chair can have any one of the remaining 5 persons : 5 ways after that, the fourth chair can have any one of the remaining 4 persons : 4 ways so total seating arrangements = 7*6*5*4

8. ganeshie8

the problem is equivalent to that of finding number of 4 letters words using 7 different letters

9. mathmath333

i think it as only 4 persons can be seated and the 4 persons can be arranged in 4! ways

10. amilapsn

Simplicity @ganeshie8 :D lol

11. ganeshie8

4! is true if you just have 4 chairs

12. amilapsn

....and only 4 people..

13. mathmath333

yes i just have 4 chairs

14. ganeshie8

** 4! is true if you just have 4 chairs and 4 people

15. amilapsn

You can take a simple example like 4 people and 3chairs and get the feeling @mathmath333

16. amilapsn

people ABCD ok? All possible ways: ABC ACB ABD ADB ACD ADC .... ... Fill in the blanks and you've get the feeling....

17. mathmath333

is there any website that shows permutations and combinations list

18. amilapsn

python has got the function permutations in itertools module.

19. mathmath333

20. ganeshie8

you may use this for combinations https://jsfiddle.net/ganeshie8/r2hjr3js/4/

21. mathmath333

nice

22. mathmath333

it gave this for abcdefg and 4 comb {a,b,c,d} {a,b,c,e} {a,b,d,e} {a,c,d,e} {b,c,d,e} {a,b,c,f} {a,b,d,f} {a,c,d,f} {b,c,d,f} {a,b,e,f} {a,c,e,f} {b,c,e,f} {a,d,e,f} {b,d,e,f} {c,d,e,f} {a,b,c,g} {a,b,d,g} {a,c,d,g} {b,c,d,g} {a,b,e,g} {a,c,e,g} {b,c,e,g} {a,d,e,g} {b,d,e,g} {c,d,e,g} {a,b,f,g} {a,c,f,g} {b,c,f,g} {a,d,f,g} {b,d,f,g} {c,d,f,g} {a,e,f,g} {b,e,f,g} {c,e,f,g} {d,e,f,g}

23. ganeshie8

right you should get 7C4 = 35 combinations

24. ganeshie8

for permutations, notice that each of that combination above can be permuted in 4! ways so number of permutations = 35*4!

25. mathmath333

is this question same as "In how many ways can a 4 digit number be formed using digits "1,2,3,4,5,6,7"

26. amilapsn

yep... If you aren't allowed to use the same number twice.

27. mathmath333

ok thnx

28. mathmath333

from the past 2 weeks i m getting this very annoying bug I have to reload the page every time to type and my question gets changed to this page

29. ganeshie8

you're not alone, everybody is facing that issue @Astrophysics is there any fix yet ?

30. amilapsn

me too...

31. mathmath333

lol how can so many people tolerate this

32. mathmath333

previuosly it happened only once in an hour but recently it get to on every long text i type