$A$ number lock on a suitcase has $3$ wheels,each labelled with $10$ digits from $0$ to $9$. If opening the lock requires a particular sequence of $3$ digits with no repeats,how many such sequences are possible?

Out of $5$ apples,$10$ mangoes,and $15$ oranges,$15$ fruits are to be distributed between two persons. Find the total number of ways of distribution.

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

Out of $7$ consonants and $4$ vowels,how many words of $3$ consonants and $2$ vowels can be formed?

If $2 \times {}^nC_5 = 9 \times {}^{n-2}C_5$,then the value of $n$ will be

The total number of $3$-digit numbers,whose sum of digits is $10$,is