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

<p>1 Captain, 1 vice-captain are already present</p> <p>$\Rightarrow$ We need to select 8 players such that atleast 3 batsman and bowler must be there</p> <p><style type="text/css"> .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} </style> <table class="tg" style="undefined;table-layout: fixed; width: 506px"><colgroup> <col style="width: 165px"> <col style="width: 129px"> <col style="width: 212px"> </colgroup> <thead> <tr> <th class="tg-7btt">Batsman</th> <th class="tg-7btt">Bowler</th> <th class="tg-7btt">Number of ways</th> </tr></thead> <tbody> <tr> <td class="tg-c3ow">3</td> <td class="tg-c3ow">5</td> <td class="tg-c3ow">${ }^6 C_3 \cdot{ }^5 C_5=20$</td> </tr> <tr> <td class="tg-c3ow">4</td> <td class="tg-c3ow">4</td> <td class="tg-c3ow">${ }^6 C_4 \cdot{ }^5 C_4=75$</td> </tr> <tr> <td class="tg-c3ow">5</td> <td class="tg-c3ow">3</td> <td class="tg-c3ow">${ }^6 C_5 \cdot{ }^5 C_3=60$</td> </tr> </tbody> </table></p> <p>Total = 155 ways</p>