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A committee of 4 is to be chosen from a group of students. If the number of students in the group increases by 1, the number of different committees triples. How many students are in the group?

May 22, 2021

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If there were n students, the number of committees would be $$nC4=\frac{n!}{4!(n-4)!}$$. You could do this by substituting different values for n . You would have only one committee if n = 4. If n= 5, the number of committees would be 5. If n=6, the number of committees would be 15. It looks like we found it, since 15 is three times 5.

If you were ambitious, you would solve the equation$$(n+1)C4=3(nC4)$$, which would translate into

$$\frac{(n+1)!}{4!(n+1-4)!}= 3(\frac{n!}{4!(n-4)!})$$

May 22, 2021