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?

Guest May 22, 2021

#1**0 **

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

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

Guest May 22, 2021