47. Forming a Committee Four members from a 20-person committee are to be selected randomly to serve as chair- person, vice-chairperson, secretary, and treasurer. The first person selected is the chairperson; the second, the vice- chairperson; the third, the secretary; and the fourth, the treasurer. How many different leadership structures are possible

116,280 different leadership structures are possible

Step-by-step explanation:

The order is important.

For example, a Committee of John, Elisa, Laura and Rose means that John is the chairperson, Elisa the vice-chairperson, Laura the secretary and Rose the treasurer. If we exchange John and Elisa, their roles are also exchanged. This means that we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

How many different leadership structures are possible

Permutations of 4 elements from a set of 20. So

116,280 different leadership structures are possible

Sue gets the largest share of 15, which is the smallest possible number of sweets Sue could get.

Step-by-step explanation:

Basil, Oscar, and Sue share 43 sweets.

Sue gets the largest share.

Let us divide the 42 sweets by 3

42/3 = 14

It means 3 equal parts of 14 make the sum 4.

i.e. 14+14+14 = 42

Since Basil, Oscar and Sue share 43 sweets, which is 1 plus 42.

So, add that 1 to Sue. i.e. 1+14 = 15

Thus, Sue gets the largest share of 15, which is the smallest possible number of sweets Sue could get.