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Question

From 4 officers and 8 privates, in how many ways can 6 be chosen (1) to include exactly one officer, (2) to include at least one officer?

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Solution

Part 1:
One officer can be choosen in 4C1 ways and remaining 5 can be chosen from 8 privates in 8C5 ways
Therefore, number of ways to choose 6 people =4C1×8C5=224

Part 2:
6 people can be chosen from 4 Officers and 8 privates in 12C6 ways
6 people can be chosen from 8 privates in 8C6 ways
Therefore, number of ways to choose 6 people with atleast 1 private = 12C68C6=92428=896

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