Question

Is anyone good with permutations? I can’t quite get the answer right for 4 b)


4. Edinburgh High School has a twelve-member student council. A four member
sub-committee is to be selected to organize dances.
a) How many different sub-committees are possible?

b) How many four member sub-committees are possible if the council
president and vice-president must be members?
han fua ouards and even forvarde on his baskethall team.

Answer 1

Answer:  $\bold{4b)\quad _{10}C_2=45\qquad\qquad 5b)\quad _4C_1\ \cdot\  _7C_3=140}$

Step-by-step explanation:

4b) 2 members are pre-selected for the subcommittee, so there are 2 spots left and 10 people remaining to choose from.  $_{10}C_2=\large\boxed{45}$

5b) 1 of the guards is pre-selected for the team, so there is only 1 spot left and 4 people remaining to choose from. There are still 3 spots for the forwards out of 7 people.     $_4C_1\ \cdot\  _7C_3=4\times 35=\large\boxed{140}$

Note: Your answers are correct for 4a and 5a