The value of $\sum_{r=0}^4 {}^{(19-r)} C_3 + {}^{15} C_4$ is equal to

If $n$ is even and the value of $^nC_r$ is maximum,then $r = $

The total number of ways of selecting $4$ letters from all the letters of the word $TSEAMCET$ is

The number of ways of choosing $10$ objects out of $31$ objects,of which $10$ are identical and the remaining $21$ are distinct,is

From all the English alphabets,five letters are chosen and are arranged in alphabetical order. The total number of ways,in which the middle letter is $M$,is:

Statement-$1$: $10$ identical balls can be distributed into $4$ distinct boxes in $^9C_3$ ways such that no box remains empty.
Statement-$2$: Any $3$ positions out of $9$ positions can be selected in $^9C_3$ ways.