amising6 wrote:itsratul wrote:A second grade class is writing reports on birds. The students' teacher has given them a list of 6 birds they can choose to write about. If Lizzie wants to write a report that includes two or three of the birds, how many different reports can she write?
Ans: 35
if she wants to write report about 2 bird she can choose this two bird
first she has 6 bird to choose from in second time she has five bird to choose 6*5=30
if she wants to write report about 3 bird she can choose this 3 bird
first she has 6 bird to choose from in second time she has five bird to choose third time she has 4 bird to choose from 6*5*4=120
so total 30+120=150
Hi,
order doesn't matter here. A report on birds AB is not different from a report on birds BA.
For two birds, 6*5, because there are 2! different ways of ordering and because we want to remove order, we would divide 6*5 by 2!, giving us 15.
Similarly, for three birds, 6*5*4, because there are 3! ways of ordering the birds and because order doesn't matter, we would divide 6*5*4 by 3!, giving us 20.
Of course, we can also solve by explicitly using the combinations formula as albatross and indiantiger did.
