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In a football team there are 10 outfield players and 2 goalkeepers. What is the probability of selecting 6 players, which includes 4 outfield players and 2 goalkeepers?


1. 23/30
2. 13/30
3. 11/35
4. 12/35
5. 7/30

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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

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