Number of different words that can be formed from all letters of word $APPLICATION$ such that two vowels never come together is -
$(45)7!$
$8!$
$6!7!$
$(32)6!$
$^{n - 1}{C_r} = ({k^2} - 3)\,.{\,^n}{C_{r + 1}}$ if $k \in $
In how many ways can $6$ persons be selected from $4$ officers and $8$ constables, if at least one officer is to be included
In a touring cricket team there are $16$ players in all including $5$ bowlers and $2$ wicket-keepers. How many teams of $11$ players from these, can be chosen, so as to include three bowlers and one wicket-keeper
A man has $7$ friends. In how many ways he can invite one or more of them for a tea party
A country has ten smart cities. The government decides to connect all these cities by road. How many roads the government need to construct so that every city is connected to every other city ?