Question

Combinatorics
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How many different solutions are here
$\pm \: 2\pm \: 2\pm \: 2\pm \:2 \pm \: 2\pm \: 2\pm \: 2$

Are you familiar with +/- sign , it's same we use in Shridharacharya quadratic formula to write 2 solution at once ​

Answer 1

EXPLAINED CLEARLY IN THE PICTURE

HOPE IT HELPS....

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Answer 2

Answer:

5040

Step-by-step explanation:

The answer is 7! = 5040

Let us understand why we have taken factorial here :-

Assume you have three boxes A, B, and C.

How many ways can we place them on top of each other?

It's 6 times

C(A, B, C)

C(A, C, B)

C(B, A, C)

C(B, C, A)

C(C, B, A)

C(C, A, B)

This is nothing but 3! = 6

By taking this simple example we can solve this problem

In total we have seven number of 2's and its value can either be '+' or '-'.

So from the before example, the blocks can either be placed on top, bottom or the middle.

In here the '+' and '-' signs can be placed in any non-repeating order just like the blocks.

Hope this solution helps:)