$^{20}C_1 + 3 ^{20}C_2 + 3 ^{20}C_3 + ^{20}C_4$ is equal to-

There are $6$ men and $8$ women in a club,and a committee of $5$ people must be formed. What will be the number of ways to select $5$ people if only men are selected?

Find how many words can be formed out of the letters of the word '$ORIENTAL$' so that vowels always occupy the odd places.

From $8$ men and $6$ women,a group of seven persons is to be formed. In how many ways can the group be formed such that the group includes at least two ladies?

Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by $66$,then the number of men who participated in the tournament lies in the interval

In how many ways can the letters of the word '$UNIVERSAL$' be arranged when $E, R, S$ are always together?