Question

no of ways in which 6 + and 4 - can be arranged such that no 2 - are together

Answer 1

... what?

Answer 2

It is a question on Permutation and combination. We need to find the no. of ways in which 6 '+' signs and 4 "-" signs can be arranged in such a way that no two '-" signs are together.

Answer 3

@zepdrix Please reply.

Answer 4

Oh boy that sounds tricky :(

Answer 5

Okay this is easy if you apply a trick.
First arrange the 6 + in 6 positions. There is only one way to do so.
+ , +, +, +,+,+
Now we want to insert the - in such a way that no two - are next to each other. Simply place the - between the +. In this way the position that - can acquire is
_+ _ + _ + _ + _ + _ +_ (_ are the places in which - can go)
There are 7 positions and 4 signs
=7P4
= 840

Answer 6

Answer is 35. How to explain that ?

Answer 7

Oh sorry it should be 7P4 / 4! = 35

Answer 8

The reason we chose to divide by 4! is because the 4 negative signs are identical.

Answer 9

Why is there only one way to put the +'s?
Hmm

Answer 10

okkkkk.. understood now. Thanks..

Answer 11

\(\color{#0cbb34}{\text{Originally Posted by}}\) @zepdrix
Why is there only one way to put the +'s?
Hmm
\(\color{#0cbb34}{\text{End of Quote}}\)
They all are identical

Answer 12

Technically there are 6P6 ways to arrange 6 objects in 6 positions. But since each object is identical to other, all permutations are identical. Thus there is only one way to arrange 6 IDENTICAL objects (in this case '+') in 6 different positions