the Pune IPL team is to be selected out of fourteen players five of them are bowlers in how many ways the team can be selected so that the team contain atleast three bowlers
Answers
Given : Pune IPL team is to be selected out of fourteen players five of them are bowlers
To find : how many ways the team can be selected so that the team contain atleast three bowlers
Solution:
Total players = 14
Bowlers = 5
other non bowler players = 14 - 5 = 9
Team has 11 Players
3 Bowlers selected = ⁵C₃ * ⁹C₈ = 90
( 3 bowlers out of 5 and 8 from 9 non bowler players)
4 Bowlers selected = ⁵C₄ * ⁹C₇ = 180
( 4 bowlers out of 5 and 7 from 9 non bowler players)
5 Bowlers selected = ⁵C₅ * ⁹C₆ = 84
(5 bowlers out of 5 and 6 from 9 non bowler players)
Total Ways = 90 + 180 + 84 = 354
354 ways team has atleast 3 bowlers
another way
total players = 11
bowlers = 5
Minimum 2 bowlers has to be selected as max 9 are non bowlers
bowlers = 2 + 9 non bowlers players is only case when 3 bowlers are not there
total cases = ¹⁴C₁₁ = 364
2 Bowlers selected = ⁵C₂ * ⁹C₉ = 10
( 2 bowlers out of 5 and 9 from 9 non bowler players)
364 - 10 = 354
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