$^nC_r + 2^nC_{r-1} + ^nC_{r-2} = $

The students in a class are seated according to their marks in the previous examination. Once,it so happens that four of the students got equal marks and therefore the same rank. To decide their seating arrangement,the teacher wants to write down all possible arrangements,one in each of separate bits of paper,in order to choose one of these by lots. How many bits of paper are required?

How many $5$-digit even numbers can be formed using the digits $1, 2, 5, 5, 4$?

$A$ father with $8$ children takes them $3$ at a time to the Zoological gardens,as often as he can without taking the same $3$ children together more than once. The number of times each child will go to the garden 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?

The total number of permutations of the letters of the word "$BANANA$" is