Use a tree diagram or systematic listing to answer the quest

Use a tree diagram (or systematic listing) to answer the question. A family has 4 children. A tree diagram or systematic list can be used to show how many ways the children could have been born, from first born to last born. The ordering of children can be described with G\'s and B\'s. For example, GGBB or GBGB. Determine how many ways the family could have had one boy and 3 girls. (Type a numerical value. For example: 25)

Solution

there are 4 children

we need to find out the number of ways the family could have 1 boy & 3 girl ,

which is same as number of ways to arrange 3G and 1B

= 4!/(3!*1!) =4

they are GGGB,GGBG,GBGG,BGGG