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There are 4 doctors and 8 lawyers in a panel. Find the number of ways for selecting a team of 6 if at least one doctor must be in the team.

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There are 4 doctors and 8 lawyers in a panel. A team of 6 with at least one doctor is to be formed.

We count the number by the INDIRECT method of counting.

Number of ways to select a team of 6 people = 12C6

Number of teams with No doctor in any team = 8C6

∴ Required number of ways = 12C68C6

= 924 – 28

= 896

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