Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# In how many ways a team of 10 players out of 22 players can be made if 6 particular players are always to be included and 4 particular players are always excluded$A){}^{22}{C_{10}}$$B){}^{18}{C_3}$$C){}^{12}{C_4}$$D){}^{18}{C_4} Last updated date: 18th Jun 2024 Total views: 403.5k Views today: 12.03k Answer Verified 403.5k+ views Hint: To solve this question, we should know the details about the non-fixed places in the team and the players who are always excluded or included. The number of ways of selecting “r” players out of players is given by{}^n{C_r}. Using this formula, we can get the answer. Complete step by step answer: In the question, It is given that a team of 10 players out of 22 players. Here are 6 particular players always to be included and 4 particular players are always excluded. Therefore, we can write the total numbers of players = 22 We have to find that we need to select the team of 10 players We have to exclude 4 particulars players of them So we have to subtract it as the total number of players Now we have only 18 players are now available. Also, from these 6 particulars will always be including. \therefore The required number of ways = {}^{12}{C_4}. Note: In these types of problems, we need to know the key concept of permutation and combination. Students can make a mistake by not considering the constraints given in the question. That leads to a selection of 10 out of 22 players which can be written as {}^{22}{C_{10}}$$ = {}^{22}{C_{22 - 10}} = {}^{22}{C_{12}}$ which leads to a wrong answer.
Generally, students get confused between permutation and combination.
If you have to select, then use a combination, and if you have to arrange use permutation. It is a very nice trick to use. Do not forget to use the correct way otherwise you will get the wrong answer.