Question -
Answer -
Given:
Total number ofplayers = 16
Number of players tobe selected = 11
So, the combinationis 16C11
By using the formula,
nCr = n!/r!(n – r)!
16C11 = 16! / 11! (16 – 11)!
= 16! / (11! 5!)
= [16×15×14×13×12×11!]/ (11! 5!)
= [16×15×14×13×12] /(5×4×3×2×1)
= 4×7×13×12
= 4368
(i) Include 2particular players?
It is told that twoplayers are always included.
Now, we have to select9 players out of the remaining 14 players as 2 players are already selected.
Number of ways = 14C9
14C9 = 14! / 9! (14 – 9)!
= 14! / (9! 5!)
= [14×13×12×11×10×9!]/ (9! 5!)
= [14×13×12×11×10] /(5×4×3×2×1)
= 7×13×11×2
= 2002
(ii) Exclude 2particular players?
It is told that twoplayers are always excluded.
Now, we have to select11 players out of the remaining 14 players as 2 players are already removed.
Number of ways = 14C9
14C11 = 14! / 11! (14 – 11)!
= 14! / (11! 3!)
= [14×13×12×11!] /(11! 3!)
= [14×13×12] / (3×2×1)
= 14×13×2
= 364
∴ The required no.of ways are 4368, 2002, 364.