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From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4 bowlers. One batsmen and one bowler who are captain and vice-captain respectively of the team should be included. Then the total number of ways such a selection can be made, is

JEE · Math · previous-year question

  1. A.145
  2. B.165
  3. C.155correct
  4. D.135

Answer

C. 155

Explanation

1 Captain, 1 vice-captain are already present $\Rightarrow$ We need to select 8 players such that atleast 3 batsman and bowler must be there .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-c3ow{border-color:inherit;text-align:center;vertical-align:top} .tg .tg-7btt{border-color:inherit;font-weight:bold;text-align:center;vertical-align:top} Batsman Bowler Number of ways 3 5 ${ }^6 C_3 \cdot{ }^5 C_5=20$ 4 4 ${ }^6 C_4 \cdot{ }^5 C_4=75$ 5 3 ${ }^6 C_5 \cdot{ }^5 C_3=60$ Total = 155 ways

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