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# Combinations

0
133
3
+321

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
+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
+31684
+2

7 C 4 = 35

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

Apr 12, 2021
#3
+113186
+2

Lets see, Catmg and EP will be right of course

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

Apr 12, 2021
edited by Melody  Apr 12, 2021