The total number of selections of the letters in the phrase "ned needs nineteen nets" is:

Let $P_m$ stand for $^nP_m$. Then the expression $1 \cdot P_1 + 2 \cdot P_2 + 3 \cdot P_3 + \dots + n \cdot P_n =$

The letters of the word $ASSASSIN$ are written down at random in a row. The probability that no two $S$ occur together is

Letters in the word $HULULULU$ are rearranged. The probability of all three $L$ being together is

Team $A$ consists of $7$ boys and $n$ girls and Team $B$ has $4$ boys and $6$ girls. If a total of $52$ single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl,then $n$ is equal to

Find the number of different signals that can be generated by arranging at least $2$ flags in order (one below the other) on a vertical staff,if five different flags are available.