In how many ways can a football team of 11 players be selected from 16 players? How many of these will

(i) Include 2 particular players?

(ii) Exclude 2 particular players?

Asked by Aaryan | 1 year ago |  33

##### Solution :-

Given:

Total number of players = 16

Number of players to be selected = 11

So, the combination is 16C11

By using the formula,

nCr =$$\dfrac{ n!}{r!(n – r)!}$$

16C11 = $$\dfrac{16! }{ 11! (16 – 11)!}$$

= 4×7×13×12

= 4368

(i) Include 2 particular players?

It is told that two players are always included.

Now, we have to select 9 players out of the remaining 14 players as 2 players are already selected.

Number of ways = 14C9

14C9 =$$\dfrac{ 14! }{ 9! (14 – 9)!}$$

= 7×13×11×2

= 2002

(ii) Exclude 2 particular players?

It is told that two players are always excluded.

Now, we have to select 11 players out of the remaining 14 players as 2 players are already removed.

Number of ways = 14C9

14C11 = $$\dfrac{ 14! }{ 11! (14 – 11)!}$$

= 14×13×2

= 364

The required no. of ways are 4368, 2002, 364.

Answered by Sakshi | 1 year ago

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