How many different numbers of $6$ digits can be formed with the digits $3, 1, 7, 0, 9, 5$?

The number of ways of selecting $15$ teams from $15$ men and $15$ women,such that each team consists of a man and a woman,is

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

The number of permutations of $n$ things taken $r$ at a time,when $p$ things are always included,is

How many words can be formed out of the letters of the word '$EDUCATION$' such that vowels occupy the odd positions?

Three horses $H_{1}, H_{2}, H_{3}$ entered a field which has $7$ portions marked $P_{1}, P_{2}, P_{3}, P_{4}, P_{5}, P_{6}$ and $P_{7}$. If no $2$ horses are allowed to enter the same portion of the field,in how many ways can the horses graze the grass of the field?