There are 12 volleyball players in all in a c | vedclass

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

Question

(D) Total number of players = $12$.Number of players to be selected for the team = $9$.Since the captain is fixed,we have already selected $1$ player.

Vedclass · Accepted Answer

$165$

Vedclass · Answer

(D) Total number of players = $12$.Number of players to be selected for the team = $9$.Since the captain is fixed,we have already selected $1$ player.Therefore,we need to select the remaining $9 - 1 = 8$ players from the remaining $12 - 1 = 11$ players.The number of ways to choose $8$ players from $11$ is given by the combination formula $^{n}C_{r} = \frac{n!}{r!(n-r)!}$.Number of ways = $^{11}C_{8} = ^{11}C_{11-8} = ^{11}C_{3}$.$^{11}C_{3} = \frac{11 	imes 10 	imes 9}{3 	imes 2 	imes 1} = 11 	imes 5 	imes 3 = 165$.Thus,the team can be formed in $165$ ways.

There are $12$ volleyball players in all in a college,out of which a team of $9$ players is to be formed. If the captain always remains the same,then in how many ways can the team be formed?

Similar Questions

The value of $\sum_{r=0}^{20} {}^{50-r}C_{6}$ is equal to

If $^{n + 1}{C_3} = 2{\,^n}{C_2},$ then $n =$

All the five-digit numbers in which each successive digit exceeds its predecessor are arranged in the increasing order of their magnitude. The $97^{th}$ number in the list does not contain the digit:

There are $6$ men and $8$ women in a club in which a committee of $5$ people has to be formed. What will be the number of ways to select $5$ people if no man is selected?

There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves exceeded the number of games that the men played with the women by $66$. The total number of participants is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module