+0  
 
0
190
3
avatar

Our football team needs to fill 4 positions. To do this, it has 10 members, of which only 3 are strong enough to play offensive lineman, while all other positions can be played by anyone. In how many ways can we choose a starting lineup consisting of a quarterback, a running back, an offensive lineman, and a wide receiver?

Guest Apr 21, 2018
 #1
avatar+963 
+1

Hello Guest!

 

Alright, first we need to take care of the positions with special conditions. 

 

The lineman has a special condition, which only three of them are strong enough to do. 

 

There are \(\binom{3}{1}\)ways to choose a lineman. 

 

The rest doesn't need any special players. 

 

So the total amount of ways is:

 

\(\binom{3}{1}+\binom{9}{1}+\binom{8}{1}+\binom{7}{1}=3+9+8+7=27\)

 

I'm pretty sure that is the final answer. 

 

I hope this helps, 

 

Gavin.

GYanggg  Apr 21, 2018
 #2
avatar+90969 
+1

Here's my best attempt......

 

Assuming that only the ones who are strong enough to play offensive lineman only play that position...

 

We have 3 ways to choose these players for this position

 

And for the other 7, we need to choose any 3 of them to man the other positions

 

So..the total starting line-ups are

 

3 * C(7,3)  =   3 * 35   =   105

 

However...if  the the offensive lineman not selected for the offensive line can also play any of the other positions we have

 

3 ways to  choose a lineman * 9 ways to fill any of the remaining 3 positions* 8 ways to choose any remaining two positions * 7 eays to  choose the last position

 

C(3,1) * C(9,1) * C(8, 1) * C(7,1)  =  3 * 9 * 8 * 7  =  1512 starting lineups

 

 

cool cool cool

CPhill  Apr 21, 2018
 #3
avatar
0

CPhi, Congrats for solving this problem correctly. You are truly a genius

Guest Apr 22, 2018

30 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.