Question

16. Determine the total number of different arrangements of three or four toys from a basket of eight different toys

17. A motorcycle licence plate consists of two or three letters followed by four digits. How many licence plates can be made?

18. A club has 18 members. In how many ways could a president, vice president, treasurer and secretary be chosen?

19. How many ways are there to select four people from a group of nine people, without regard to order?

20. In how many ways can 4 cards be chosen from a deck of 52, if the order in which they are chosen does not matter?

21. You found seven library books that you would like to take out, but the maximum is four. In how many ways could you select four books?

Answer 1

16) We have to find out the total number of different arrangements of three or four toys from a basket of eight different toys. So, here we have to find . So, here we will get two cases.

From the first case, we will find the total number of different arrangements of three toys from a basket of eight different toys. Here, n = 8, r = 3.

From the permutation formula, we have,  

Thus, here = (8!)/(5!) = (8*7*6*5!)/(5!) = 336

From the second case, we will find the total number of different arrangements of four toys from a basket of eight different toys. Here, n = 8, r = 4.

Thus, = (8!)/(4!) = (8*7*6*5*4!)/(4!) = 1680

Thus, the total number of arrangements is,

= 1680 + 336 = 2016.