How many numbers lying between $999$ and $10000$ can be formed with the help of the digits $0, 2, 3, 6, 7, 8$ when the digits are not to be repeated?

How many words can be formed from the letters of the word $COURTESY$,whose first letter is $C$ and the last letter is $Y$?

In a city,no two persons have an identical set of teeth,and there is no person without a tooth. Also,no person has more than $32$ teeth. If we disregard the shape and size of the teeth and consider only the presence or absence of a tooth at each of the $32$ positions,then the maximum population of the city is:

In how many ways can a team of $10$ players be selected from $22$ players if $6$ particular players are always to be included and $4$ particular players are always excluded?

Out of $6$ boys and $4$ girls,a group of $7$ is to be formed. In how many ways can this be done if the group is to have a majority of boys?

If $^nC_{r-1} = 36$,$^nC_r = 84$,and $^nC_{r+1} = 126$,then the value of $r$ is