Correct Answer - Option 3 : 11/35
Given:
Number of out field players = 10
Number of goalkeepers = 2
Selecting players = 6
Selecting outfield players = 4
Selecting goalkeepers = 2
Formula Used:
(A) The probability of occurrence of an event E, within a sample space S, is given by:
P(E) = n(E) / n(S)
where P(E) = probability of occurrence of the event E,
n(E) = number of times the event E occurs, and
n(S) = number of points in the sample space S.
(B)Distributing n things among r persons so that any of them can get none one, two or all = (n + r - 1)C(r - 1)
nCr = { n! / [r! × (n - r)!]}
Calculation:
⇒ Number of ways to select 2 players = 12C2 = 66 ---(∵ Total number of players in the team = (10 + 2) = 12)
⇒ Number of ways to select 2 players = 66
⇒ Number of ways to select 4 outfield players = 10C4 = 210 ---(∵ Total number of outfield players = 10)
⇒ Number of ways to select 4 outfield players = 210
⇒ Number of ways to select 2 goalkeepers = 2C2 = 1 ---(∵ Total number of goalkeepers = 2)
⇒ Number of ways to select 2 goalkeepers = 1
⇒ Required probability = (66 × 1)/210
∴ Required probability = 11/35