The value of $^{15}C_3 + ^{15}C_{13}$ is

The number of ways in which $10$ persons can go in two boats so that there may be $5$ on each boat,supposing that two particular persons will not go in the same boat is:

In how many different ways can the letters of the word '$LEADING$' be arranged in such a way that the vowels always come together?

In how many ways is it possible to choose a white square and a black square on a chess board so that the squares do not lie in the same row or column?

$^{14}C_4 + \sum_{j=1}^4 {^{18-j}C_3}$ is equal to

If ${}^n{P_4} : {}^n{P_5} = 1 : 2$,then $n = $