There are 15 stations on a train route and th | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The total number of ways to choose $5$ stations out of $15$ is given by ${ }^{15} C_5$. To find the number of ways where no two stations are conse

Vedclass · Accepted Answer

${ }^{15} C_5 - { }^{11} C_5$

Vedclass · Answer

(C) The total number of ways to choose $5$ stations out of $15$ is given by ${ }^{15} C_5$. To find the number of ways where no two stations are consecutive,we use the gap method. Let the $10$ stations where the train does not stop be represented by $X$. $X_1 X_2 X_3 X_4 X_5 X_6 X_7 X_8 X_9 X_{10}$ There are $11$ possible gaps (including the ends) where we can place the $5$ stations where the train stops. The number of ways to choose $5$ gaps out of $11$ is ${ }^{11} C_5$. Thus,the number of ways in which the train stops at at least two consecutive stations is the total ways minus the ways where no two stations are consecutive: $= { }^{15} C_5 - { }^{11} C_5$.

There are $15$ stations on a train route and the train has to be stopped at exactly $5$ stations among these $15$ stations. If it stops at at least two consecutive stations,then the number of ways in which the train can be stopped is

Similar Questions

The number of $5$-digit natural numbers such that the product of their digits is $36$ is:

The remainder obtained when $1! + 2! + 3! + \dots + 11!$ is divided by $12$ is

If $\alpha = ^mC_2$,then $^\alpha C_2$ is equal to

The total number of three-digit numbers,divisible by $3$,which can be formed using the digits $1, 3, 5, 8$,if repetition of digits is allowed,is:

$A$ box contains $5$ blue, $6$ yellow, and $4$ red balls. The number of ways of drawing $8$ balls containing at least two balls of each color is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module