about to only mathematics

Options

A. `""^(8)C_(5)xx5!`
B. `""^(7)C_(5)xx5!`
C. `""^(8)C_(5)`
D. `7!`

Answer

C

Explanation

We want to separate minus signs. So, let us first arrage 7 plus signs in a row. This can be done in `(7!)/(7!)=1` ways as shown below.

A blank box in the above arrangement shows available space for minus signs. Clearly, there are eight blank boxes in which we have to arrange minus signs. This can be done in
`""^(8)C_(5)xx(5!)/(5!)=""^(8)C_(5)` ways
`:.` Number of all possible arrangements `=1xx""^(8)C_(5)=""^(8)C_(5)``=1xx""^(8)C_(5)=""^(8)C_(5)`