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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 doubles. How many students are in the group?

 Apr 12, 2021
 #1
avatar+1329 
+2

Let x be the number of students. 

 

2*(x)(x-1)(x-2)(x-3)/24 = (x+1)(x)(x-1)(x-2)/24

2(x-3) = (x+1)

2x-6 = x+1

x = 7

 

I hope this helped. :))

 

=^._.^=

 Apr 12, 2021
 #2
avatar+31684 
+2

7 C 4 = 35

8 C 4 = 70        there were 7 in the original group

 Apr 12, 2021
 #3
avatar+113186 
+2

Lets see, Catmg and EP will be right of course   wink

 

\((n+1)C4 = 2*nC_4\\ \frac{(n+1)!}{4!(n+1-4)!}=2*\frac{n!}{4!(n-4)!}\\ \frac{n!(n+1)}{4!(n-4)!(n-4+1)}=2*\frac{n!}{4!(n-4)!}\\ \frac{(n+1)}{(n-4+1)}=2*\frac{1}{1}\\ \frac{(n+1)}{(n-3)}=2\\ n+1=2n-6\\ -n=-7\\ n=7\)

 Apr 12, 2021
edited by Melody  Apr 12, 2021

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