Page 119 - Probability Demystified

108 CHAPTER 6 The Counting Rules

There are 16 C 3 ways to select 3 people from 16 people.

16! 16! 16 15 14 13!
C ¼ ¼ ¼ ¼ 560
16 3
ð16 3Þ!3! 13!3! 13! 3 2 1
20 1
Pð3 womenÞ¼ ¼ 0:036
560 28

2. There are 3 C 1 ways to select a defective toaster and 9 C 3 ways to select
3 nondefective toasters.

3! 9! 3! 9!
1
3
9
3 C C ¼ ¼ ¼ 3 84 ¼ 252
ð3 1Þ!1! ð9 3Þ!3! 2!1! 6!3!
There are 12 C 4 ways to select 4 toasters from 12 toasters.
12! 12! 12 11 10 9 8
C ¼ ¼ ¼ ¼ 495
12 4
ð12 4Þ!4! 8!4! 8! 4 3 2 1
252
Hence, P(1 defective toaster and 3 nondefective toasters) ¼ ¼
28 495
0:509
55

3. There are 2 C 2 ways to win 2 prizes.
2! 2!
2 C ¼ ¼ ¼ 1
2
ð2 2Þ!2! 2!
There are 100 C 2 ways to give away the prizes

100! 100 99 98!
C ¼ ¼ ¼ 4950
100 2
ð100 2Þ!2! 98! 2 1
1
Pðwinning both prizesÞ¼ ¼ 0:0002
4950

4. There are 6 C 2 ways to select the nurses, and 4 C 1 ways to select the
doctors.
6! 4!
C C ¼ ¼ 15 4 ¼ 60
6 2 4 1
4!2! 3!1!