If $^nC_3 + ^nC_4 > ^{n+1}C_3$,then

In how many ways can a committee consisting of one or more members be formed out of $12$ members of the Municipal Corporation?

$A$ committee of $4$ persons is to be formed from $2$ ladies,$2$ old men,and $4$ young men such that it includes at least $1$ lady,at least $1$ old man,and at most $2$ young men. The total number of ways in which this committee can be formed is:

The number of ways in which $35$ apples can be distributed among $3$ boys so that each can have any number of apples,is

If $\alpha = \binom{m}{2}$,then $\binom{\alpha}{2} = \dots$

The total number of all those $3$-digit numbers in which the sum of all the digits in each of them is $10$,is