How many words of $4$ consonants and $3$ vowels can be formed from $6$ consonants and $5$ vowels
$75000$
$756000$
$75600$
None of these
If ${a_n} = \sum\limits_{r = 0}^n {} \frac{1}{{^n{C_r}}}$ then $\sum\limits_{r = 0}^n {} \frac{r}{{^n{C_r}}}$ equals
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
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?
There are two urns. Urm $A$ has $3$ distinct red balls and urn $B$ has $9$ distinct blue balls. From each urm two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is
If $^{2017}C_0 + ^{2017}C_1 + ^{2017}C_2+......+ ^{2017}C_{1008} = \lambda ^2 (\lambda > 0),$ then remainder when $\lambda $ is divided by $33$ is-