EXPLAIN THE FOLLOWING:

A committee of 6 is to be selected from 6 lawyers and 9 engineers. In how many ways:

a) can 2 lawyers and 4 engineers be chosen to form the committee?

(6C2)(9C4) = 1890

b) 3 lawyers and 3 engineers?

(6C3)(9C3) = 1680

c) 6 engineers?

(6C0)(9C6) = 84

d) all lawyers?

(6C6)(9C0) = 1

In how many ways can 40 students choose their seats in a room with 5 rows of chairs, each row containing 10 chairs if they can sit:

a) in any of the 50 seats?

(50P40) = 8.381308753 x 1057

b) if the last row has to be left vacant?

(40P40) = 8.159152832 x 1047

In how many ways can one select 5 Philippine stamps and 4 Australian stamps from 15 Philippine stamps, 12 American stamps and 9 Australian stamps and then arrange them on 9 spaces in a stamp album?

> (15C5) (12C0) (9C4) (9P9) = 1.373058086 x 1011

Roy is planning to buy a new car. He has a choice of 3 engine makes, 7 body styles and

14 different colors. How many different cars does he have to choose from?

> (3) (7) (14) = 294

It is required to seat 5 men and 5 women in a row of 10 chairs so that the women occupy the even-numbered seats. How many such arrangements are possible?

> (5P5) (5P5) = 14400

A mountain to be observed for bio-diversity was divided into 25 observation quadrats. In

how many ways can a biologist select 5 quadrats for observation and plan his transfer from

quadrat to quadrat?

> (25C5) (5P5) = 6375600 OR 25P5 = 6375600

With 12 airlines to choose from for the trips, in how many ways can Mr. Lo travel from

Manila to Sydney and back to Manila:

a) if he chooses not to travel on the same airline on his way back?

(12C1)(11C1) = 132

b) if he chooses to travel on the same airline on his way back?

(12C1)(1) = 12