Five oys and three girls are sitting in a row of `8` seats. Number of ways in which they can be seated so that not all the girls sit side by side is

Correct Answer - `(5)/(7)` Total number of ways is `7!` Favorable number of ways is `7! - 2 (6!)`. Hence, the probability is `(7! - 2(6!))/(7!) = 1 - (2)/(7) =...

Correct Answer - D Three-digit numbers are 100, 101, …, 999. Total number of such numbers is 900. The three-digit numbers (which have all same digits) are 111, 222, 333, …,...

Correct Answer - A Total number of cases = `5!` Since `S_(1)` gets seat `R_(1)` and none of the other gets previously allotted seat, we have derangement of 4 students. So,...

Correct Answer - 9 cm Let the length of the shotest side of the triangle be x cm . Then length of the longest side = 3 x cm Length of...

Correct Answer - C `(c )` The boys can be seated in `5!` ways. If the girls `g_(1)` and `g_(2)` do not want to sit by the side of `A_(1)` (say)....

Correct Answer - A `(a)` The possible arrangements of teachers and students can be as follows : `(i) T S S T S S T S S` `(ii) S T S...

Correct Answer - A `(a)` First arrange `12` persons `A_(4),A_(5),….A_(15)` in `"^(15)P_(12)` ways There remains `3` places. Keep `A_(1)` in the first place and arrange `A_(2)`, `A_(3)` in the remaining two...

Correct Answer - C `(c )` First arrange `8` blue alike bottles `to ` number of ways `=1` Now select one gap out of `9` gaps created to put two green...

Correct Answer - C `(c )` Case I : When no box remains empty Then number of ways of distribution is `.^(10-1)C_(5-1)=^(9)C_(4)=126` Case ii : Exactly one box is empty Number...

Correct Answer - 43200