The number of ways in which 3 men and 3 women can be arranged in a row of 6 seats, such that the first and last seats must be filled by men is

If a committee of 10 members is to be formed from 8 men and 6 women, then the number of different possible committees in which the men are in majority is

If the eleventh term in the binomial expansion of $(x+a)^{15}$ is the geometric mean of the eighth and twelfth terms, then the greatest term in the expansion is

The sum of the rational terms in the binomial expansion of $\left(\sqrt{2}+3^{1 / 5}\right)^{10}$ is