All possible numbers are formed using the digits $1, 1, 2, 2, 2, 2, 3, 4, 4$ taken all at a time. The number of such numbers in which the odd digits occupy even places is

The number of arrangements of the letters of the word $BANANA$ in which two $N$s do not appear adjacently is

If a man and his wife enter a bus in which five seats are vacant,then the number of different ways in which they can be seated is

Let $n > 2$ be an integer. Suppose that there are $n$ Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track. Further,each pair of nearest stations is connected by a blue line,whereas all remaining pairs of stations are connected by a red line. If the number of red lines is $99$ times the number of blue lines,then the value of $n$ is

All possible four-digit numbers are formed using the digits $0, 1, 2, 3$ such that no digit is repeated. The number of even numbers among them is

The number of $7$-digit numbers which can be formed using the digits $1, 2, 3, 2, 3, 3, 4$ is: