<p>"From a group of 6 Juniors and 8 Seniors on the student council, 2 juniors and 4 seniors will be chosen to make a 6 person team.
How many different 6-team committees are possible?"
A) 84
B) 85
C) 1,050
D) 1,710
E) 1.890</p>
<p>The book says the answer is C, 1,050. The explanation has to do with factorials, the explanation is 15*70=1050. I tried permutations and got a crazy high number like 6000 something. Any help on solving like problems and a more thorough explanation would be incredible.</p>
<p>Same, I am in AP Calc and I’ve never been taught combinations, factorials, or permutations. I think the last time I heard about permutations was for about 2 days in 6th grade.</p>
<p>First, we separately choose 2 juniors and 4 seniors.
In mathematics, a combination is a way of selecting k things out of a group of n things where the order does not matter. It can be found using the following formula
C<em>n^k=n!/k!(n-k)!
Therefore, the number of ways to choose 2 juniors from 6 is
C</em>6^2=6!/2!4!=(5<em>6)/(2</em>1)=15
The number of ways to choose 4 juniors from 8 is
C_8^4=8!/4!4!=(5<em>6</em>7<em>8)/(4</em>3<em>2</em>1)=70
Using the product rule, we get the number of different 6-team committees
15*70=1050
Answer: 1050.</p>
<p>First, we separately choose 2 juniors and 4 seniors.
In mathematics, a combination is a way of selecting k things out of a group of n things where the order does not matter. It can be found using the following formula
C<em>n^k=n!/k!(n-k)!
Therefore, the number of ways to choose 2 juniors from 6 is
C</em>6^2=6!/2!4!=(5<em>6)/(2</em>1)=15
The number of ways to choose 4 juniors from 8 is
C_8^4=8!/4!4!=(5<em>6</em>7<em>8)/(4</em>3<em>2</em>1)=70
Using the product rule, we get the number of different 6-team committees
15*70=1050
Answer: 1050.</p>
</p>