The number of odd positive divisors of $67500$ is

The number of sequences of ten terms,whose terms are either $0$,$1$,or $2$,that contain exactly five $1$s,exactly three $2$s,and two $0$s,is equal to:

Three players play a total of $9$ games. In each game,one person wins and the other two lose; the winner gets $2$ points and the losers get $-1$ each. The number of ways in which they can play all the $9$ games and finish each with a zero score is

The coefficient of $x^{10}$ in the expansion of $(x+\frac{2}{x}-5)^{12}$ is

If a proper divisor of the integer $2520$ is selected at random,then the probability that it is an odd number is

The number of $6$-digit numbers of the form $ababab$ (in base $10$) each of which is a product of exactly $6$ distinct primes is