Question

Combinatorics problem, show all work.

a. There are 25 varieties of cereal and I'm going to pick six different kinds to bring home to the family. How many ways can I do that?

b. Forty students compete in an essay contest. There will be a blue ribbon, a red ribbon, and a yellow ribbon (for first, second, and third place) and four "honorable mentions" that get white ribbons. How many ways are there to award prizes to the students.

Answer 1

a)

number of ways to pick r object out of n = nCr

here n = 25 , r = 6

hence

25C6 is correct

b)

B,R,Y, (WWWW)

= 40 * 39 * 38 * 37C4

{

40*39*38 for selecting three student and arranging got three different position
now 37 students are left
we have to pick 4 for extra award in 37C4 ways
note that positions are same
hence we have to pick only , no arrangement }