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To deal with this item, let us summarize the details of the problem:
(a) Syllabus area: Permutation and Combination
(b) Formula/Concept needed:
> Permutation or Combination
> Addition of Probabilities
Before we answer the items, let us encircle the important clues/phrases.
It means that:
Next is
It means that:
The first case is that there is only one (1) woman. It means that five (5) men are needed to complete the team of 6. The total number of possible selections are:
The first case is that there are two (2) women. It means that four (4) men are needed to complete the team of 6. The total number of possible selections are:
The first case is that there are three (3) women. It means that three (3) men are needed to complete the team of 6. The total number of possible selections are:
Adding the number of possible selections:
Hence, there are 203 teams that could be formed with 6 members and at least one woman.
Another method is to consider all possible number of teams with 6 members that can be formed out of the 10. Here are the possible teams that could be formed without restrictions.
Let us separate the teams formed into two.
Since we are only interested on the number of teams with at least one woman, we could deduct the number of teams without any woman from the total. That is
The total number of teams formed with 6 members (no restriction) is
The total number of teams formed with 6 members without a woman is
Subtracting them,
Hence, the total number of teams formed with 6 members with at least one woman is 203.
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Another method is to consider all possible number of teams with 6 members that can be formed out of the 10. Here are the possible teams that could be formed without restrictions.
or
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Your comments and suggestions are welcome here. Write them in the comment box below.
Thank you and God bless!
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