There are $5$ students in class $10,6$ students in class $11$ and $8$ students in class $12.$ If the number of ways, in which $10$ students can be selected from them so as to include at least $2$ students from each class and at most $5$ students from the total $11$ students of class $10$ and $11$ is $100 \mathrm{k}$, then $\mathrm{k}$ is equal to $......$
$240$
$245$
$270$
$238$
In an election there are $5$ candidates and three vacancies. A voter can vote maximum to three candidates, then in how many ways can he vote
How many words, with or without meaning, each of $3$ vowels and $2$ consonants can be formed from the letters of the word $INVOLUTE$?
In how many ways can $6$ persons be selected from $4$ officers and $8$ constables, if at least one officer is to be included
Determine the number of $5 -$ card combinations out of a deck of $52$ cards if each selection of $5$ cards has exactly one king.
It is required to seat $5$ men and $4$ women in a row so that the women occupy the even places. How many such arrangements are possible?