Question

The number of ways in which p positive signs may be placed in a row so that no two negative signs shall be together is

• A. ${}^{p+1}{C}_n$
• B. ${}^p{C}_n$
• C. ${}^{p-1}{C}_n$
• D. None of these

Answer 1

Answer: (A)

${}^{p+1}{C}_n$

We have,

Suppose that,

$p=10$ positive signs and $n=4$ negative signs.

Then,

So the answer for this is specific case is ${}^n{C}_r$.

So, the answer is $(p+1)$ choose $n$ which is also called the number of combinations of $(p+1)$ things taken n at a time.

It is sometimes written ${}^{p+1}{C}_n$.

Hence, this is the required answer.