How many ways can a 2-person subcommittee be selected from a committee of 7 people? The number of ways can a president and vice president is?

Question

How many ways can a 2-person subcommittee be selected from a committee of 7 people? I need help with this problem please

Answer 1

Use the combination rule of n!/k!(n-k)! where n is the number of options (7) and k is the number of slots (2).

 

Do this if the order does not matter.

 

7!/2!(7-2)! = 7*6*5*4*3*2*1/2*1*(5*4*3*2*1) = 7*6/2 = 21

 

If, however, the order does matter, then use the permutation rule of n!/(n-k!) with n = 7 and k =2 giving 7*6 = 42.