If $^nP_5 = 9 \times ^{n-1}P_4$,then the value of $n$ is

The number of four-digit natural numbers which contain exactly two distinct digits is:

$A$ box contains two white balls,three black balls,and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?

How many $4$-digit numbers are there with distinct digits?

In how many ways can the letters of the word '$ALGEBRA$' be arranged when both $A$ do not come together?

How many $2$-digit odd numbers can be formed from the digits $1, 2, 3, 4, 5$ and $8$,if repetition of digits is allowed?