MediumMathematicsHigh School (11–12)Algebra › Permutations and CombinationsNumericalBoard ExamA-LevelIB
A committee of 5 is chosen from 6 men and 5 women. How many committees have at least 2 women?
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A committee of is chosen from men and women. How many committees have at least women?
Need a reminder? The key ideaShow
If someone must be in, choose the rest from the others; if someone must be out, choose from the others. Choices from separate groups multiply. For "at least one", subtract the selections with none from the total. To make words or codes, select first, then arrange the chosen things in ways.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. All committees. .
Step 2. No woman. .
Step 3. Exactly one woman. .
Step 4. Subtract. .
Answer: committees.
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