$A$ father with $8$ children takes them $3$ at a time to the Zoological gardens,as often as he can without taking the same $3$ children together more than once. The number of times he will go to the garden is

The number of different $6$-digit numbers that are divisible by $10$,which can be formed using the digits $1, 2, 7, 0, 9, 5$?

There are $8$ students appearing in an examination of which $3$ have to appear in a Mathematics paper and the remaining $5$ in different subjects. In how many ways can they be made to sit in a row if the candidates in Mathematics cannot sit next to each other?

If $12 \cdot {}^{n}C_{2} = {}^{2n}C_{3}$,find $n$.

In a club election,the number of contestants is one more than the number of maximum candidates for which a voter can vote. If the total number of ways in which a voter can vote is $62$,then the number of candidates is:

Find the number of arrangements of the letters of the word '$ALGEBRA$' without altering the relative position of the vowels and the consonants.