Question

3. An arborist knows how to graft any two citrus trees together. Suppose that she has 8 types of citrus trees in her tree farm. If you want a tree with 2 citrus trees grafted together, how many choices are there?

Answer 1

since you have 8 different types of tree lets name them A,B,C,D,E,F,G,H

NOW we want to know in how many ways we can graft two citrus trees together.

if we use combinattorial analysis it is simple i.e

total number of ways =8_C2 =8!/2!6! =28

8c₂ =total number of ways of selecting 2 trees out 8 trees

in more clear way

total number of ways={AB,AC,AD,AE,AF,AG,AH,BC,BD,BE,BF,BG,BH,CD,CE,CF,CG,CH,DE,DF,DG,DH,EF,EG,EH,FG,FH,GH}

hence there are total 28 choices of grafting two trees together out of 8 different types of tree.