How many integers between $1000$ and $10000$ have no digits other than $4, 5,$ or $6$?

There are $5$ letters and $5$ directed envelopes. Find the number of ways in which the letters can be put into the envelopes so that all are not put in directed envelopes?

How many permutations can be made by using all the letters of the word $MATHEMAGICA$?

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

$A$ person $X$ has four notes of $1, 2, 5,$ and $10$ denominations. The number of different sums of money she can form from them is

How many words can be formed from the letters of the word $COURTESY$,whose first letter is $C$ and the last letter is $Y$?