Question

7. For each of the following questions, indicate whether the question posed involves permutations or combinations. Then, provide an answer to the question with an explanation for your

choice.
a. A student club has 20 members. How many ways are there for the club to choose a president and a vice president?
b. A football team of 50 players will choose two co-captains. How many different ways are there to choose the two co-captains?
c. There are seven people who meet for the first time at a meeting. They shake hands with each other and introduce themselves. How many handshakes have been exchanged?
d. At a particular restaurant, you must choose two different side dishes to accompany your meal. If there are eight side dishes to choose from, how many different possibilities are there?
e. How many different four-letter sequences can be made using the letters A, B, C, D, E, and F if letters may not be repeated?

Answer 1

a.380

b.1225

c.21

d.28

e.360

Explanation:

a. In this problem permutation is used because order is important. The president and vice president plays different role in a club committee. So, nPr=20P2=20!/18!=380 .

b.In this problem combination is used because order is not important. The two co-captains plays same role in a football team. So, nCr=50C2=50!/2!*48!=1225.

c.In this problem combination is used because order is not important. The hand shakes made are unique. So, nCr=7C2=7!/2!*5!=21.

d.In this problem combination is used because order is not important. The two side dishes order does not matter. So, nCr=8C2=8!/2!*6!=28.

e.In this problem permutation is used because order is important. There is no repetition of letters and every sequence of letter will be unique even with same letters such as BCDE and EDCB are different still have same letters . So, nPr=6P4=6!/2!=360.