A scientific committee is to be formed from $6$ Indians and $8$ foreigners, which includes at least $2$ Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed, is
$1625$
$575$
$560$
$1050$
The number of words not starting and ending with vowels formed, using all the letters of the word $'UNIVERSITY'$ such that all vowels are in alphabetical order, is
The number of arrangements that can be formed from the letters $a, b, c, d, e,f$ taken $3$ at a time without repetition and each arrangement containing at least one vowel, is
At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are $10$ candidates and $4$ are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is
If $P(n,r) = 1680$ and $C(n,r) = 70$, then $69n + r! = $
Total number of $3$ letter words that can be formed from the letters of the word $'SAHARANPUR'$ is equal to