Question -
Answer -
Given:
Total number ofplayers = 16
Number of players tobe selected = 11
So, the combinationis┬а16C11
By using the formula,
nCr┬а= n!/r!(n тАУ r)!
16C11┬а= 16! / 11! (16 тАУ 11)!
= 16! / (11! 5!)
= [16├Ч15├Ч14├Ч13├Ч12├Ч11!]/ (11! 5!)
= [16├Ч15├Ч14├Ч13├Ч12] /(5├Ч4├Ч3├Ч2├Ч1)
= 4├Ч7├Ч13├Ч12
= 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 =┬а14C9
14C9┬а= 14! / 9! (14 тАУ 9)!
= 14! / (9! 5!)
= [14├Ч13├Ч12├Ч11├Ч10├Ч9!]/ (9! 5!)
= [14├Ч13├Ч12├Ч11├Ч10] /(5├Ч4├Ч3├Ч2├Ч1)
= 7├Ч13├Ч11├Ч2
= 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 =┬а14C9
14C11┬а= 14! / 11! (14 тАУ 11)!
= 14! / (11! 3!)
= [14├Ч13├Ч12├Ч11!] /(11! 3!)
= [14├Ч13├Ч12] / (3├Ч2├Ч1)
= 14├Ч13├Ч2
= 364
тИ┤┬аThe required no.of ways are 4368, 2002, 364.