The number of $4-$letter words, with or without meaning, each consisting of $2$ vowels and $2$ consonants, which can be formed from the letters of the word $UNIVERSE$ without repetition is $.........$.
$431$
$430$
$432$
$487$
In how many ways can a student choose a programme of $5$ courses if $9$ courses are available and $2$ specific courses are compulsory for every student?
A person is permitted to select at least one and at most $n$ coins from a collection of $(2n + 1)$ distinct coins. If the total number of ways in which he can select coins is $255$, then $n$ equals
$^{47}{C_4} + \mathop \sum \limits_{r = 1}^5 {}^{52 - r}{C_3} = $
The value of $\sum\limits_{r = 1}^{15} {{r^2}\,\left( {\frac{{^{15}{C_r}}}{{^{15}{C_{r - 1}}}}} \right)} $ is equal to
The number of ways of choosing $10$ objects out of $31$ objects of which $10$ are identical and the remaining $21$ are distinct, is