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

If ${}^nC_{r-1}=36$,${}^nC_r=84$,and ${}^nC_{r+1}=126$,then the value of $nr^2$ is

$^nC_{r+1} + ^nC_{r-1} + 2^nC_r = \dots$

If ${ }^{2n}C_3 : { }^{n}C_3 = 12 : 1$,then $n =$

In how many ways can we select any $4$ letters from the word $CORGOO$?

The number of groups that can be made from $5$ different green balls,$4$ different blue balls,and $3$ different red balls,if at least $1$ green and $1$ blue ball must be included.