In how many ways can a cricket team of 11 pla | vedclass

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

Question

(A) Total players available = $16$.We need to select a team of $11$ players.Given conditions:$1$. $2$ particular players must be included.$2$. $1$ par

Vedclass · Accepted Answer

$715$

Vedclass · Answer

(A) Total players available = $16$.We need to select a team of $11$ players.Given conditions:$1$. $2$ particular players must be included.$2$. $1$ particular player must be rejected.Since $2$ players are already included,we need to select $11 - 2 = 9$ more players.Since $1$ player is rejected and $2$ are already included,the number of players remaining to choose from is $16 - 2 - 1 = 13$.Therefore,the number of ways to select the remaining $9$ players from $13$ players is given by the combination formula ${}^{n}C_{r} = \frac{n!}{r!(n-r)!}$.Number of ways = ${}^{13}C_{9} = {}^{13}C_{13-9} = {}^{13}C_{4}$.${}^{13}C_{4} = \frac{13 	imes 12 	imes 11 	imes 10}{4 	imes 3 	imes 2 	imes 1} = 13 	imes 11 	imes 5 = 715$.

In how many ways can a cricket team of $11$ players be selected out of $16$ players if $2$ particular players are to be included and $1$ particular player is to be rejected?

Similar Questions

The number of ways in which an arrangement of $4$ letters of the word $PROPORTION$ can be made is

If the letters of the word $MOTHER$ are permuted and all the words so formed (with or without meaning) are listed as in a dictionary,then the position of the word $MOTHER$ is

$A$ committee of $5$ members is to be formed out of $3$ trainees,$4$ professors,and $6$ research associates. In how many different ways can this be done if the committee must have $2$ trainees and $3$ research associates?

For a set of $5$ true-or-false questions,no student has written all the correct answers,and no $2$ students have given the same sequence of answers. What is the maximum number of students in the class,for this to be possible?

The number of ways in which $3$ boys and $4$ girls can be seated around a circular table if no two boys sit together is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module