Combination and permutation questions

[cmal]

q1. in how many ways can a team of 11 players be selcted out of 16 including 2 particular players.?


q2. in how many ways can a team of 11 players be selcted out of 16 excluding 2 particular players.?

[kmittal82]

q1)

Since 2 players must be there, you effectively have to chose 9 players out of 14

This can be done in 14C9 ways

q2)

Total number of ways to select 11 players out of 16 = 16C11
Total number of ways to select a team including 2 particular players (as found in q1) = 14C9

Thus, total number EXCLUDING two particular players = 16C11 - 14C9

OA please?

[goyalsau]

q1)

Total number of ways to select 11 players out of 16 = 16C11
Total number of ways to select a team including 2 particular players (as found in q1) = 14C9

Thus, total number EXCLUDING two particular players = 16C11 - 14C9

OA please?

Can you please explain why it will not be 14C11

[sanju09]

q1)

Since 2 players must be there, you effectively have to chose 9 players out of 14

This can be done in 14C9 ways

q2)

Total number of ways to select 11 players out of 16 = 16C11
Total number of ways to select a team including 2 particular players (as found in q1) = 14C9

Thus, total number EXCLUDING two particular players = 16C11 - 14C9

OA please?

good reasoning in Question 1, kmittal82, but this is missing in Question 2, I'm sorry. When 11 players be selcted out of 16 excluding 2 particular players, you effectively have to chose 11 players out of 14

This can be done in 14C11 ways, in your kind words

[kmittal82]

q1)

Since 2 players must be there, you effectively have to chose 9 players out of 14

This can be done in 14C9 ways

q2)

Total number of ways to select 11 players out of 16 = 16C11
Total number of ways to select a team including 2 particular players (as found in q1) = 14C9

Thus, total number EXCLUDING two particular players = 16C11 - 14C9

OA please?

good reasoning in Question 1, kmittal82, but this is missing in Question 2, I'm sorry. When 11 players be selcted out of 16 excluding 2 particular players, you effectively have to chose 11 players out of 14

This can be done in 14C11 ways, in your kind words

right you are sanju, my bad... but then what did I just find? :roll:

[sanju09]

q1)

Since 2 players must be there, you effectively have to chose 9 players out of 14

This can be done in 14C9 ways

q2)

Total number of ways to select 11 players out of 16 = 16C11
Total number of ways to select a team including 2 particular players (as found in q1) = 14C9

Thus, total number EXCLUDING two particular players = 16C11 - 14C9

OA please?

good reasoning in Question 1, kmittal82, but this is missing in Question 2, I'm sorry. When 11 players be selcted out of 16 excluding 2 particular players, you effectively have to chose 11 players out of 14

This can be done in 14C11 ways, in your kind words

right you are sanju, my bad... but then what did I just find? :roll:

Just the same answer brainy, but I found your way analogous to using my right hand for picking penny out of the left-hand cross pocket of the jeans that I'm having on now.

[kmittal82]

q1)

Since 2 players must be there, you effectively have to chose 9 players out of 14

This can be done in 14C9 ways

q2)

Total number of ways to select 11 players out of 16 = 16C11
Total number of ways to select a team including 2 particular players (as found in q1) = 14C9

Thus, total number EXCLUDING two particular players = 16C11 - 14C9

OA please?

good reasoning in Question 1, kmittal82, but this is missing in Question 2, I'm sorry. When 11 players be selcted out of 16 excluding 2 particular players, you effectively have to chose 11 players out of 14

This can be done in 14C11 ways, in your kind words

right you are sanju, my bad... but then what did I just find? :roll:

Just the same answer brainy, but I found your way analogous to using my right hand for picking penny out of the left-hand cross pocket of the jeans that I'm having on now.

16C11 - 14C9 = 2366
14C11 = 364

[cmal]

Right

QI) Ans is 14C 9

Q2) Ans is 14c11