Problem Solving

1. From a group of 21 astronaut that includes 12 people with previous experience in space flight, a 3 person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crew of this type is possible?
a. 432
b. 594
c. 864
d. 1330
e. 7980

2 Machine A produces pencils at a constant rate of 9,000 pencils an hour and machine b produces at a constant rate of 7,000 pencils an hour. If both machines are to combine to produce 100,000 pencils, how long will machine B operate at a minimum, if either machine can work at most 8 hours.
a. 4
b. 4 2/3
c. 5 1/3
d. 6
e. 6 ¼

let machine A work for the maximum time i.e. 8 hrs
in 8 hrs machine a can produce 72000 pencils
remaining 100000-72000 = 28000 pencils
Machine B produces 7000 pencils in 1 hr
to produce 28000 pencils, it must work 4 hrs
hence A

Q1. 12C1 * 9C2 = 432
hence A

IMO 1 . A 2.A

1. Total people = 21
Experienced [E] = 12
Non - exp [N] = 21- 12 = 9
3 people are to be chosen with eaxctly 1 E and 2N

__ X __ X __

12 X 9 X 8
--------------
2

= 432


2. A's speed = 9000 pencil / hr
B's speed = 7000 pencil / hr

Minimum operating time for either machine is 8 hrs , but we need to minimize B's effort so we have to maximize A's effort .
=> A 's work for 8 hrs = 72,000 pencils

Pencils left to make 100,000 - 72,000 = 28000

Time B has to work = 28000/ 7000 = 4 hrs.