Question

(A) How many ways can a 2-person subcommittee be selected from a committee of 8 people?

Answer 1

To solve this problem, we have to use the combination formula

`C^r_n=(n!)/(r!(n-r)!)`

Where r represents the number of people for the subcommittee (2), and n represents the total committee (8). Replacing this information, we have

`C^2_8=(8!)/(2!(8-2)!)=(8!)/(2!(6)!)`

Remember that factorials are solved by multiplying the number in a reversal way, as follows

`C^2_8=(8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1)/((2\cdot1)(6\cdot5\cdot4\cdot3\cdot2\cdot1))=(40,320)/(2(720))=(40,320)/(1,440)=28`

Therefore, there are 28 ways to form a 2-person subcommittee from a committee of 8.