Sum

Answer the following:

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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#### Solution

We count the number by INDIRECT method of counting.

Number of ways to select a team of 6 people = ^{12}C_{6}

Number of teams with No doctor in any team = ^{8}C_{6}

Required number = ^{12}C_{6} – ^{8}C_{6}

= 924 – 28

= 896

Concept: Properties of Combinations

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