We know that, the coefficient of the middle term is the numerically greatest coefficient in the expansion of (1−x)n or (1+x)n and its value is nCn∕α or
nCn+1
2
=
nCn−1
2
according as n iseven or odd. It is given that the coefficient of the 5 th term is the greatest. Therefore, 5 th term is the middle term. Thus, there are 9 terms. Hence, n=8.