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.
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